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Information-theoretic security offered by the wiretap channel model has been extensively studied for various scenarios recently. One scenario that has not received much attention is secrecy for systems with memory in the form of input constraints or inter-symbol interference (ISI). In this work, we consider finite state wiretap channels (FSWCs), which model the scenario of secrecy with memory. Using results on secrecy capacity for arbitrary wiretap channels, we first arrive at the secrecy capacity of a FSWC. Then, we develop a stochastic algorithm for computing tight lower bounds on the secrecy capacity of a less-noisy FSWC, and illustrate the computation through examples. Our results provide numerical comparisons between secrecy capacities with and without memory, and provide specific targets for code design.