Abstract: Two simple integral equation methods are proposed for the analysis of vertical loaded pile. One of them is; let the axisymmetrical loads formed by Mindlin's horizontal point forces be distributed along the axis z in [0, L] of the elastic half-space, and composed with the Boussinesq's point force. The other is: in addition to the above fictitious loads, the. Mindlin's vertical forces are distributed along the axis z in [0, L]. The former reduces the problem of a vertical loaded pile embedded in a half-space with the following boundary conditions.

Key words: second-order nonlinear differential equation, delay, Liapunov functional