Optimization Modulo Theories ( OMT ) is an extension of SMT which allows for finding models that optimize given objectives. OptiMathSAT is an OMT solver which allows for solving a list of optimization problems on SMT formulas with linear objective functions—on the Boolean, the rational and the integer domains, and on their combination thereof—including (partial weighted) MaxSMT . Multiple and heterogeneous objective functions can be combined together and handled either independently, or lexicographically, or in linear or min–max /max–min combinations. OptiMathSAT provides an incremental interface, it supports both an extended version of the SMT-LIBv2 language and a subset of the FlatZinc language, and can be interfaced via an API. In this paper we describe OptiMathSAT and its usage in full detail.