This paper discusses solving the forward problem for electrical resistance tomography (ERT). The mathematical model is governed by Laplace's equation with the most general boundary conditions forming the so-called complete electrode model (CEM). We examine this problem in simply-connected and multiply - connected domains (rigid inclusion, cavity and composite bi-material). This direct problem is solved numerically using the boundary element method (BEM) and the method of fundamental solutions (MFS). The resulting BEM and MFS solutions are compared in terms of accuracy, convergence and stability. Anticipating the findings, we report that the BEM provides a convergent and stable solution, whilst the MFS places some restrictions on the number and location of the source points.