Abstract In this paper, two new approximation functions are introduced. These new techniques, which are referred herein as the multi-triangles method (MTM) and weighted multi-triangles method (WMTM) are applied for the approximation of unknowns and their derivatives at the points of interest. The approximations are performed in terms of the unknowns corresponding to the field nodes which are the vertices of the region surrounding the desired point and determined by Delaunay triangulations. The capability and accuracy of the proposed approximation functions are compared with the other approximating techniques in the meshless finite volume (MFV) frame work for some benchmark problems. Numerical examples reveal the superiority of the WMTM and MTM over the common moving least squares technique (MLS) and radial point interpolation method (RPIM) for the same number of nodes in the support domain. Moreover, the suggested methods need less computational time especially when dense field nodes are applied.