An evaluation stack, used exclusively to store temporary values in expression evaluation, is known to be an effective mechanism in the implementation of high level languages. This work considers the efficient management of evaluation stacks for concurrent programming languages. Techniques for sharing a single evaluation stack among many processes, without copying on process switches, are developed. The best strategy for managing the evaluation stack is shown to depend strongly upon the scheduling paradigm adopted by the run-time support of the language. Simulation studies, driven by synthetic workloads, show that the techniques described in this paper exhibit substantial performance improvements over traditional temporary storage management schemes for concurrent languages.