Bituminous materials exhibit either one or a combination of viscous, elastic, and viscoelastic responses. When applied loads are limited, the materials’ behavior can be considered linear. For higher loads they exhibit a nonlinear response. In relation to pavement performance, understanding the behavior of the binders for loads corresponding to the magnitude and frequency of the truck loading is important. With the framework of porous asphalt (PA) application, this paper investigates the behavior of a bituminous mortar at various temperatures and shear stress levels. A dynamic shear rheometer setup with specimen geometry specially designed for mortar testing was used. The mortar, which consisted of bitumen, filler, and fine fractions of sand, was produced according to a standard PA mixture recipe. Various measurements conducted at the linear viscoelastic range showed that the utilized setup provided very good test result repeatability. The nonlinear behavior was obtained by performing tests at high shear stress levels. The observed nonlinear behavior was described by using Schapery nonlinear theory. To allow numerical use, a three-dimensional form of the theory was implemented in ABAQUS by using user material subroutines. For code verification, time and frequency domain simulations were performed to reproduce the experimental data. Good comparisons between simulated and measured data were obtained. The paper presents the details of the laboratory and numerical studies and also discusses the theoretical implications of the results for PA design.