The Boundary Element Method presents difficulties for solving certain problems that include sources, body and inertia forces or other cases whose mathematical model includes non self-adjoint terms. This avoids the desired representation of the problem solely in terms of boundary integrals. In this work, a new strategy is presented to overcome that problem through the use of Radial basis functions. Two formulations of this kind are used for solving the distribution of the pressure field generated in a hydrodynamic journal bearing. The partial differential equation of this problem has variable coefficients and cannot be rewritten directly as boundary integrals. Numerical solutions for the 1D and 2D problems are presented and their results are compared with the available analytical solutions or then obtained with the application of the finite element method.