Based on the basic differential equations of a flexible pile and the C-method assumption, a power series solution of the internal forces and displacements of a flexible pile in a single homogeneous soil was obtained under inclined loads, taking the weight of the pile and its shaft resistance into account. The foundation coefficient was assumed to be parabolic to the depth of subgrade in the C-method. The flexural responses of the pile were compared with the results calculated by the traditional m-method in an engineering example. The results have indicated the internal forces and displacements of a flexural pile calculated with the power series solution are well consistent with those in practical engineering. And the maximum bending moment of the pile and the horizontal displacement of the ground based on C-method have been elevated by 10%, compared with those obtained in m-method.