Summary: Finite model and counter model generation is a potential alternative in automated theorem proving. In this paper, we introduce a system called FMSET which generates finite structures representing models of equational theories. FMSET performs a satisfiability test over a set of special first-order clauses called “simple clauses”. The algorithm’s originality stems from the combination of a standard enumeration technique and the use of first-order resolution. Our objective is to obtain more propagations and still achieve good space and time complexity. Several experiments over a variety of problems have been pursued. FMSET uses symmetry to prune from the search tree unwanted isomorphic branches.