This paper deals with the three-dimensional numerical solution of composite heat transfer problems using meshless element free Galerkin method (EFG). The EFG method utilizes moving least square (MLS) approximants to approximate the unknown function of temperature T(x) with T-h(x). These MLS approximants are constructed by using a weight function, a basis function and a set of non-constants coefficients. Variational method is utilized for the discretization of the governing equations. The essential boundary conditions are enforced using Lagrange multiplier technique. The MATLAB codes have been developed to obtain the numerical solution. The EFG results are obtained for a model problem using different weight functions. Three new weight functions namely exponential, rational and cosine have been proposed. A comparison is made among the results obtained using proposed (exponential, rational and cosine) and existing (R&R, cubic spline, quartic spline, Gaussian, quadratic and hyperbolic) EFG weight functions with finite element method (FEM) for a three-dimensional composite heat transfer model problem. The validation of the EFG code has been achieved by comparing the EFG results with those obtained by FEM. The effect of scaling parameter on EFG results has also been discussed. (C) 2004 Elsevier Ltd. All rights reserved.