The aim of this study is to develop a computational model to analyze thermally induced stress and deformation in a heat generating solid rod. The rod is initially at zero temperature, but for times greater than zero heat is generated internally at both space and time dependent rate. As the rod is heated up slowly an uncoupled solution is realized. The heat conduction equation with a variable generation rate is solved by a finite element collocation method. Two different generation rates are handled. The numerical solution of thermoelastic equation is achieved by a shooting method. The computational model is verified in comparison to analytical solution for a special case.