© 2017 IEEE. Novel architectures for massively parallel machines offer better scalability and the prospect of achieving linear speedup for sizable problems in many domains. The development of suitable programming models and accompanying software tools for these architectures remains one of the biggest challenges towards exploiting their full potential. We present a multi-layer software abstraction model to develop combinatorial solvers on massively-parallel machines with regular topologies. The model enables different challenges in the design and optimization of combinatorial solvers to be tackled independently (separation of concerns) while permitting problem-specific tuning and cross-layer optimization. In specific, the model decouples the issues of inter-node communication, n ode-level scheduling, problem mapping, mesh-level load balancing and expressing problem logic. We present an implementation of the model and use it to profile a Boolean satisfiability solver on simulated massively-parallel machines with different scales and topologies.