Summary: A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of pore-dynamic problems considering elastic and elastoplastic materials. Formulations adopting the Heaviside step function as the test functions in the local weak form are considered. The moving least-square method is used for the approximation of physical quantities in the local integral equations. After spatial discretization is carried out, a nonlinear system of time-domain ordinary differential equations is obtained. This system is solved by Newmark/Newton-Raphson techniques. The present work is based on theu-p formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the interstitial fluid pore pressures. Independent spatial discretization is considered for each phase of the model, rendering a more flexible, efficient and robust methodology. At the end of the paper, numerical applications illustrate the accuracy and potentialities of the proposed techniques.