The paper deals with the comparison of two approaches that use global interpolation with radial basis functions (RBF) combined with the collocation technique to solve interface problems. The latter arise when the domain of the problem consists of two or more different materials/media that are in contact forming an interface. Across this interface a discontinuity of material parameters arises which is difficult to catch using the methods based on global interpolation. On the other hand, such methods are characterized by high rate of convergence and, in the strong form formulation, are easy to implement. These advantages were the motivation to modify a meshless collocation method that uses RBF to make it useful in solving such problems. So far, this method was successfully applied to problems characterized by smooth solutions [1]. In order to extend the usefulness of the method to interface problems, two approaches have been proposed. One of them divides the entire domain into subdomains where the problem is homogeneous. Then, the discretization is carried out separately in each subdomain. With proper interface conditions, the solutions from the subdomains are combined. The other approach modifies the RBF using so-called discontinuous scaling function [2, 3]. In this way we obtain a global interpolant possessing discontinuity across the interface. By using this interpolant within conventional formulation of the method, a non-smooth or discontinuous solution can be obtained. Recent numerical tests confirm the effectiveness of the approach. In the present work the described approaches are compared by solving several differential equations due to the accuracy, convergence and stability of the solution process. REFERENCES [1] W. Chen, Z.J. Fu, C.S. Chen, Recent Advances in Radial Basis Function Collocation Methods. Springer, 2014. [2] S. De Marchi, et al, Shape-driven interpolation with discontinuous kernels: error analysis, edge extraction and applications in MPI. SIAM Journal on Scientific Computing, 42(2), B472-B491, 2020. [3] A. Krowiak and J. Podgórski, A modified kernel-based collocation method for interface boundary value problems, Computer Methods in Applied Mechanics and Engineering, submitted for publication.