A boundary-discontinuous double Fourier series method for obtaining analytical solutions to the problems of deformation of finite moderately thick cross-ply doubled-curved panels, with four different boundary constraints, is presented in Part I of this investigation. In this segment, the equations that arise by way of satisfying these boundary conditions, thereby ensuring well-posedness of the formulation and existence of the solutions thus obtained, are presented first. The convergence characteristics of the series solutions, especially their dependence on laminations and boundary constraints, are then numerically investigated in detail. Other numerical results presented here include (i) verification/comparison with the available FSDT (first-order shear deformation theory)- and CLT (classical lamination theory)-based analytical solutions, (ii) investigation of the effects of length-to-thickness and radius-to-length ratios on the response of antisymmetric and symmetric cross-ply doubly-curved panels, with various boundary constraints, and (iii) spatial variation of displacements, rotations and moments.