The meshless local Petrov-Galerkin method (MLPG) with a mixed formulation to impose Dirichlet boundary conditions is investigated in this paper. We propose the use of Shepard functions for inner nodes combined with the radial point interpolation method with polynomial terms (RPIMp) for nodes over the Dirichlet boundaries. Whereas the Shepard functions have lower computational costs, the RPIMp imposes the essential boundary conditions in a direct manner. Results show that the proposed technique leads to a good tradeoff between computational time and precision.