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将桩机为弹性杆件．推导了其在轴向和侧向荷载作用下的拉氏空间基本解，应用互等定理分别建立了桩在轴向和侧向动力荷载作用下的积分方程使其离散。对于土域应用了弹性半空间的拉氏空间动力基本解．采用加权残量法建立了土域的积分方程也使其离散，按照土和桩接触面的平衡和相容条件，对桩、土系统建立一组代数方程，则在其接触面和城内任意点的位移和力可以求解，由Koisumi数值求逆的方法可以得到时域的解．
The pile driver for the elastic rod. The basic solution of Lagrangian space under axial and lateral loads is deduced. The integral equation of pile under axial and lateral dynamic loads is established by using the reciprocal theorem to make them discrete. The basic solution to the Laplace space dynamics with elastic half-space is applied to the soil. The weighted integral method is also used to establish the integral equation of soil so that it is discrete. Based on the balance and compatible conditions of the contact surface between soil and pile, a set of algebraic equations are established for pile and soil systems. The displacement and force can be solved by Koisumi numerical inversion method can get the solution in time domain.