Due to their important role in many diseases, cysteine proteases represent new promising drug targets. An important class of cysteine-protease inhibitors is derived from the naturally occurring compound E64, possessing an epoxysuccinyl moiety as warhead. Experimental studies show stereoselectivity concerning the inhibition potency, e.g., a trans-configured epoxide ring is essential for inhibition, and furthermore, in most cases, the ( S, S)-configured inhibitors have a higher inhibition potency than their ( R, R)-counterparts. However, the underlying effects are not fully understood. In this work, such effects are investigated by classical molecular dynamics simulations and combined quantum mechanics/molecular modeling (QM/MM) calculations for the E64c-cathepsin B complex. Our computations reveal that the hydrogen bonding network between the enzyme and the E64c (or its derivatives) determines the stereoselectivity of the subsequent ring opening reaction by governing the distance between the attacking thiolate and the attacked C2 atom of the epoxide ring. For the ( S, S)-configuration, a strong network can be realized which enables a close contact between the reacting centers, so that the irreversible step becomes very efficient. The ( R, S)-configuration ( cis-configuration) can only form networks in which the two reacting centers are so far away from each other that the irreversible step can hardly happen. The ( R, R)-configuration is in between, less optimal than the ( S, S)-configuration but much better than the ( R, S)-configuration. Exceptions where the ( R, R)-configurations shows higher potency than the ( S, S) ones are also explained.