In the present communication the nonlinear static deflection analysis of an orthotropic shallow spherical shell resting on a Winkler-Pasternak elastic foundation, is presented. Thus, the problem is reduced to the solution of a nonlinear integro-differential equation, while several other types of nonlinear integral equations used in many other applied mechanics problems, have been proposed in the past by the author and V. A. Zisis [Existence and uniqueness for nonlinear singular integral equations used in fluid mechanics (to appear)] and the author [Nonlinear parabolic integral equations used in stationary and dyamic viscoplasticity (to appear)]. Therefore, the above mentioned nonlinear integro-differential equation is numerically evaluated by using a Chebyshev polynomials technique.