A dynamic boundary-value problem of coupled thermoelasticity for a finite cylinder with mixed boundary conditions is solved. The problem is reduced to a system of four singular integral equations solved by the mechanical-quadrature method. A numerical experiment is conducted to obtain amplitude-frequency characteristics for finite cylinders with different cross sections. The effect of thermoelastic coupling on stress distribution is assessed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 86–95, October 2006.