Based on the deformation features of three-dimensional conical strain wedge of pile side sand, the nonlinear p–y curve of laterally loaded pile in sand was obtained. Constructing the stress system of the front surface of the conical wedge and introducing the hyperbolic stress-strain model of the soil, the expression of lateral soil resistance was derived by considering the horizontal force balance in the plane of the strain wedge. On this basis, the theoretical derivation method of nonlinear p–y curve of laterally loaded pile was established by combining with the finite difference numerical analysis of a beam on elastic foundation. The case analysis of bored and driven model piles using the proposed method shows that the nonlinear p–y curves obtained by the proposed method are closer to the model test results than the p–y curves of API code, hyperbolic p–y curves and the p–y curves obtained by traditional non conical strain wedge model. By comparing the difference between the conical deformation mode and the traditional non conical strain wedge mode and analyzing the effects of pile-soil parameters, the advantages of this method are further demonstrated.