Working memory processes are important for analytic problem-solving; however, their role in multiply-constrained problem-solving is currently debated. This study explored individual differences in working memory and successful completion of analytic and multiply-constrained problem-solving by having participants solve algebra and compound remote associate (CRAT) problems of varying difficulty under low and high memory demand conditions. Working memory was predictive of both algebra and multiply-constrained problem-solving. Specifically, participants with high working memory solved more problems than those with low working. Memory load did not differentially affect performance for low and high working memory participants. However, for multiply-constrained problem-solving the effect of item difficulty was more detrimental for high-span participants than low-span participants. Together, these findings suggest that working memory processes are important for both types of problem-solving and that participants with low working memory capacity may need to offload internal memory demands onto the environment to efficiently solve problems.