The boundary element method (BEM) is known as an accurate and efficient numerical approach for wave analysis, and several variants have been developed to overcome its inherent drawbacks. The method of fundamental solutions (MFS) is one such variant of BEM, which avoids the evaluation of singular integrals arising in the BEM formulation. The MFS is a mesh-free numerical technique for solving partial differential equations, in which the solution is represented as a linear combination of fundamental solutions with unknown coefficients. These coefficients are determined so as to satisfy the prescribed boundary conditions using a collocation method. The MFS has been successfully applied to various kinds of problems, including potential problems, heat conduction, acoustic waves, and elastic waves. In recent years, non-classical elastic theories have attracted considerable attention from various viewpoints in several engineering fields. In particular, the nonlocal elasticity plays an important role in micro- and nanomechanics, where the internal and external characteristic lengths are comparable. Eringen’s nonlocal elasticity is a representative mechanical model within the framework of non-classical elastic theories. In this theory, the nonlocal stress is expressed as a convolution-type integral of the local (classical) stress with a nonlocal kernel. The nonlocal kernel decays with the distance between the interaction points, and its characteristics are governed by the internal and external length scales of the target material. In this study, we propose an MFS-based method for solving two-dimensional wave scattering problems in Eringen’s nonlocal elastic body. Numerical examples show that the proposed method can simulate wave scattering phenomena, and the effects of nonlocal characteristics on wave scattering are discussed.