The effect of curvature and polar orthotropy on nonlinear dynamic behaviour of a shallow spherical shell is investigated in the present paper. Numerical solutions based on an assumed two-term modeshape for the axisymmetric, forced (uniform pressure) and free vibrations are obtained for different shell geometries and orthotropic material constants. The results, when specialised for the case of isotropic material, are in good agreement with those available in the literature. Based on a one-term modeshape solution, the values of the geometric parameter at which the transition from hardening to softening type of nonlinearity takes place and where the reversal of the softening trend occurs are obtained for different values of the orthotropic constants. © 1978.