He was born on 3 January 1889 in Sanok,[1][a] then within the Kingdom of Galicia and Lodomeria; the son of Roman Vetulani, a high school professor, and Matylda née Pisz (1861–1891).

He had five younger, half-siblings: brothers Zygmunt (1894–1942), Tadeusz (1897–1952) and Adam (1901–1976), and sisters Maria (master of economics, clerk of the Agricultural Bank in Kraków, 1895–1945)[5][6] and Elżbieta (1903–1921, died of tuberculosis).

[2] In the first half of 1914 he lectured on explosives engineering, including blowing up bridges and railroads, at the officer training courses of the Polish Rifle Squads in Vienna.

After the Peace of Riga of March 1921, he lectured at the Technical College of Railway Forces[c] and at the courses of professional and reserve officers in Kraków.

[2] In the 1921/1922 academic year, Kazimierz Vetulani was employed as an assistant at the Mining Academy in Kraków, where he lectured in strength of materials.

[18] Then he worked as a technical advisor to a number of large companies, enterprises and central and local government institutions as well as private clients.

[2] In the same year, he obtained Ph.D. in technical sciences at the Lviv Polytechnic[g] upon the dissertation On jets of liquid, supervised by Wojciech Rubinowicz.

[2] On 1 September 1938, he became deputy professor at the Department of General Mechanics at the Faculty of Civil and Water Engineering of the Lviv Polytechnic.

[2] In the same year, the Lviv Polytechnic requested the Ministry of Religious Denominations and Public Enlightenment of Poland to present Vetulani for the nomination as full professor of general mechanics at the Faculty of Civil and Water Engineering.

The Faculty Council applied to the Minister for approval of the application regarding the right for Kazimierz Vetulani to lecture in the field of general and technical mechanics.

[2] On the night of 3 July 1941, Kazimierz Vetulani was arrested by the Gestapo and shot along with a group of professors from Lviv universities at the Wuleckie Hills.

The execution was carried out by the Einsatzkommando zur besonderen Verwendung (task force for special use) under the command of Brigadeführer Karl Eberhard Schöngarth.

Some of the Gestapo men broke a window in the second apartment on the ground floor (which was still occupied by a tenant - a Jewish woman) and went up the staircase, and some finally crashed the gate.

In just a moment (I stood with my mother at the door and looked through the case) Gestapo men were coming down the stairs with Professor Vetulani, whose figure could be recognized in the dark.

[2] According to the authors of his biography in Wiadomości Matematyczne, Vetulani “also showed great understanding of technical problems by writing papers on practical engineering issues.

This is evidenced, for example, by his opinion on the cause of the cracks, the receding and tilting of the wing of the parallel bridgehead on the river Dłubnia of the Kraków-Miechów railway line, and a technical opinion issued in print on the utility of the stone from Mogielnica for communication and construction purposes (...), as well as a lecture on the foundation of the fourth bridge on the Vistula, delivered at the Technical Society in Kraków”.

[2] Austro-Hungary Poland Kazimierz Vetulani's name was on memorial plaques and other objects commemorating the murders of professors from Lviv universities.

[30] In 1962, Kazimierz Vetulani was commemorated among other people mentioned on the plaque of the Mausoleum of Victims of World War II at the Central Cemetery in Sanok.