Any continuous function f(E) can be expanded in a Chebyshev series. The nth derivative of the function f(0 can be written in matrix form in terms of the expansion coefficients of the function. Also, the product of two functions f(E) and g(0 can be written in matrix form in terms of the expansion coefficients of the two functions. Therefore, any system of differential equations with variable coefficients can be written as a system of algebraic equations in terms of Chebyshev coefficients of the functions, which can be easily solved. The method is used to solve the problem of isotropic conical shell with different loads and boundary conditions. Results are computed and compared with the exact ones. Comparison proves  onvergence, accuracy and reliability of the proposed method.