State-of-the-art SMT solvers are highly complex pieces of software with performance, robustness, and correctness as key requirements. Complementing traditional testing techniques for these solvers with randomized stress testing has been shown to be quite effective. Re-cent work has showcased the value of input fuzzing for finding issues, but typically does not comprehensively test a solver’s API. Previous work on model-based API fuzzing was tailored to a single solver and a small subset of SMT-LIB. We present Murxla, a comprehensive, modular, and highly extensible model-based API fuzzer for SMT solvers. Murxla randomly generates valid sequences of solver API calls based on a customizable API model, with full support for the semantics and features of SMT-LIB.It is solver-agnostic but extensible to allow for solver-specific testing and supports option fuzzing, cross-checking with other solvers, translation toSMT-LIBv2, and SMT-LIBv2 input fuzzing. Our evaluation confirms its efficacy in finding issues in multiple state-of-the-art SMT solvers.