A new method for the analysis of nonlinear, large amplitude vibration of shallow shells of arbitrary shape is presented. The basic equations are derived using the concept of iso-amplitude contour lines approach. The coupled system of governing equations thus obtained, is solved using the Galerkin approach. As an illustration of the procedure, the case for a shallow dome upon an elliptical base is discussed. Some comparison is also made with previously obtained results, as available in the literature. The paper deals with first fundamental mode of vibrations only. The other mode of vibrations are not interested here as it requires to obtain the equations of iso-amplitude contour lines.