The Glamorgan Problem Solver (GLAM-PS), an example of a computationally implemented theory of embodied cognition, is a novel cognitive architecture that has been applied to algebra problem solving, Tower of London problem solving and Stroop Tasks. GLAM-PS is a distributed production system architecture, with all modules playing a role either in perception or action. Each module has its own working memory, production memory and production matching bottleneck. Inter-module communication allows each module to see the working memory of other modules and to coordinate action with activity in other modules. Despite the lack of explicit goal representation the architecture is able to model offline multi-step problem solving in algebra. Action representations are used to hierarchically structure action in Tower of London problem solving, allowing ‘subgoaling’ of particular disks. Performance on Stroop Tasks highlights the architecture’s ability to model controlled behaviour. These domains demonstrate GLAM-PS potential for providing insights into human behaviour.