A satisfactory reproduction of three-point bending and impact test data of an industrially important amorphous polymer, acrylonitrile-butadiene-styrene (ABS), in the context of finite element analysis is of prime importance to industry. Constitutive material models developed for amorphous polymers are capable of describing their complex mechanical behavior under multiaxial loadings with a variety of success; therefore, the computational accuracy directly depends on the selection of constitutive model and a proper determination of its associated parameters. Thus, this study aimed at accurately predicting the multiaxial mechanical behavior of ABS by the Anand–Gurtin elastic–viscoplastic material model selected as the constitutive model and employed for the first time in the numerical implementations of the three-point bending and impact tests of ABS. To this end, the constitutive model parameters never identified for ABS before was first determined mainly depending on uniaxial compression test data at various strain rates ranging from 2 × 10−4 s−1 to 2 × 10−1 s−1 and then validated against tension test data for a broad range of strain rates varying from 1 × 10−3 s−1 to 45 s−1. All the experimental data taken into consideration in this study was taken from the previous studies of authors. The material model with the validated constitutive parameters of ABS was utilized in the numerical implementation of three-point bending tests for two different bending speeds (0.05–10 mm/s), in addition, impact tests for two various low impact velocities (4.43–6.23 m/s). Numerical results revealed that the constitutive model successfully reproduces the three-point bending test data of ABS for both bending speeds but acceptably overestimates the impact response of ABS under both low impact velocities in terms of peak impact load. Hence, it was concluded that this computationally inexpensive complex material model with the constitutive parameters determined for ABS can be used in the accurate prediction of its multiaxial material behavior.