Abstract Due to their robustness in handling the inherent singularity difficulties associated with crack analysis, mesh-reduction methods present an avalanche of formulations in the literature which, sometimes, entails modifications to their conventional/standard forms for better results. Although such formulations provide a pool of alternative choices to the analyst, increase in their number requires some relative assessment between them in order to guarantee optimum choice of analysis tool. The present study assesses the applicability and relative performance of three such mesh-reduction methods, namely the radial basis function (RBF) method, the boundary element method (BEM), and the method of fundamental solution (MFS) for mode III crack analysis. In order to have a common ground for performance comparison, these methods are, first, tested in their most basic forms and simplest conventional formulations possible. Failure of some of them to provide reliable results calls for some enrichments. Yet, unless where necessary, efforts are made to ensure that unnecessary computationally expensive formulations are avoided. Consequently, the BEM formulation is not altered in any way, and modifications to both the RBF and MFS are limited to enrichment by the addition of, at most, one singular term and/or the domain-decomposition technique. Verification is achieved using the literature results and/or those obtained by FEM in this study. Summary of the relative advantages and limitations of the methods for mode III crack analysis is given to serve as a yard-stick based on which the choice of one over the others may be influenced.