Elastic analysis of shells of revolution subjected to thermal and mechanical loads is attempted using axisymmetric conical shell element. Non-axisymmetric thermal and mechanical loads are also considered in the form of Fourier series. A finite element program is developed in C programming language. Several problems have been solved to demonstrate the method and the results are validated with numerical tests on problems solved by classical and other methods. A cylinder heated along a meridional strip is solved using Fourier series decomposition. Also, a hyperbolic cooling tower shell subjected to non-axisymmetric wind pressure is analyzed. Effect of thermal load on the stress resultants of a cooling tower is investigated and shown to be significant enough to be taken into account in design. An interface program to a finite element post-processor is developed for further processing of the output data for graphical display of results in three-dimensional form.