Computational modeling is critical to medical device development and has grown in its utility for predicting device performance. Additionally, there is an increasing trend to use absorbable polymers for the manufacturing of medical devices. However, computational modeling of absorbable devices is hampered by a lack of appropriate constitutive models that capture their viscoelasticity and postyield behavior. The objective of this study was to develop a constitutive model that incorporated viscoplasticity for a common medical absorbable polymer. Microtensile bars of poly(L-lactide) (PLLA) were studied experimentally to evaluate their monotonic, cyclic, unloading, and relaxation behavior as well as rate dependencies under physiological conditions. The data were then fit to a viscoplastic flow evolution network (FEN) constitutive model. PLLA exhibited rate-dependent stress–strain behavior with significant postyield softening and stress relaxation. The FEN model was able to capture these relevant mechanical behaviors well with high accuracy. In addition, the suitability of the FEN model for predicting the stress–strain behavior of PLLA medical devices was investigated using finite element (FE) simulations of nonstandard geometries. The nonstandard geometries chosen were representative of generic PLLA cardiovascular stent subunits. These finite element simulations demonstrated that modeling PLLA using the FEN constitutive relationship accurately reproduced the specimen’s force–displacement curve, and therefore, is a suitable relationship to use when simulating stress distribution in PLLA medical devices. This study demonstrates the utility of an advanced constitutive model that incorporates viscoplasticity for simulating PLLA mechanical behavior.