Petro Yasniy was born in 1952. His nationality was Ukrainian. In 1973 he graduated from Lviv Polytechnic Institute in specialty "Technology of mechanical engineering, metal cutting machines and tools". After completion of his postgraduate studies he worked at the Institute for Problems of Strength of the Academy of Sciences of the Ukrainian SSR as a junior researcher from 1980 and as a senior researcher from 1983. From 1992 he worked permanently at Ternopil Instrument-Making Institute (now Ternopil Ivan Puluj National Technical University).  He worked his way up from the head of the materials science department, the vice rector for scientific work (1993–2007) to the rector of the university (from 2007). He defended theses for obtaining the scientific degree of candidate of technical sciences (in 1980) and the scientific degree of doctor of technical sciences (in 1990) in the specialty 02.01.04 - mechanics of deformable solids. In 1985 he was awarded the academic title of senior researcher, and in 1996 he was awarded the academic title of professor. He worked part-time as the head of the Department of Materials Science (from 1993), as the head of the Department of Structural Mechanics (from 2009), from 2014 as professor of the Department of Structural Mechanics, and from 2020 as professor of the Department of Mechanical Engineering Technologies. From 2007 he was the president of the Ternopil Regional Branch of the Junior Academy of Sciences of Ukraine, and from 2011 the president of the science park "Innovation and investment cluster "Ternopillia".

Petro Yasniy was well known in Ukraine and abroad for his scientific results in the field of fracture mechanics, strength and durability of materials and structural elements. Petro Yasniy created theoretical basis and developed methods of forecasting of the influence of load history, in particular, preliminary plastic deformation, single and multiple overloads on the strength and durability of bodies with cracks under conditions of quasi-static loading, fatigue, short-term and dynamic creep.

With the application of the scientific approaches and methods proposed above, he performed a number of important applied studies devoted to the assessment of the strength, serviceability and residual resource of the responsible elements of the equipment of thermal and nuclear energy industry, aviation, railway transport and metallurgy. He developed an original methodology for increasing the quasi-brittle strength of heat-resistant steels, which is based on a combined preliminary thermomechanical load, provides an increase in the effect of thermal overload compared to known methods, and at the same time reduces the maximum stresses in the structure.

Petro Yasniy published 340 printed works, including 8 monographs and 15 patents, 4 scientific and methodological manuals. There were published 109 scientific works in journals included in the SCOPUS database.  Much attention was paid to the training of young personnel. He trained 15 candidates and 2 doctors of science.

Petro Yasniy was Honored Worker in Science and Technology of Ukraine (2006), Laureate of the State Prize of Ukraine in Science and Technology (2012), Corresponding Member of the National Academy of Sciences of Ukraine (2018).

Petro Yasniy was a Member of the Council of the Western Scientific Center of the Ministry of Education and Science of Ukraine and the National Academy of Sciences of Ukraine, the Scientific Council on the Problem "Mechanics of Deformable Solids" of the National Academy of Sciences of Ukraine.

He was a member of the European Structural Integrity Society (ESIS) from 2004 and co-chairman of Technical Committee 13 "Education and Training" from 2015.

He was an honorary professor at the Lublin Polytechnic, Poland from 2020.

Petro Yasniy was the chairman of the specialized academic council C58.052.01 for the defense of candidate’s from 1996 and of the specialized academic council D58.052.01 for the defense of doctoral theses in the specialties 01.02.04 – mechanics of deformable solids and 01.05.02 – mathematical modeling and computational methods (technical sciences) from 2014 at Ternopil Ivan Puluj National Technical University. He was the editor-in-chief of the scientific journal "Scientific journal of the Ternopil National Technical University", member of the editorial boards of international scientific journals "Mathematical methods and physicomechanical fields", "Physicochemical mechanics of materials", collection of scientific works "Reliability and life of machines and structures", Acta Mechanica et Automatica.