Thermoset resin-based composite materials are widely used in the aerospace industry, mainly due to their high stiffness-to-weight and strength-to-weight ratios. A major issue with the use of thermoset resins in fiber composites is the process-induced residual stresses that are formed from resin chemical shrinkage during the curing process. These residual stresses within the composite material ultimately result in reduced durability and residual deformations of the final product. Polybenzoxazine (PBZ) polymer resins have demonstrated near-zero volumetric shrinkage during the curing process. Although the low shrinkage of PBZ is promising in terms of reduced process-induced residual stresses, little is known about the physical causes. In this work, Molecular Dynamics (MD) simulations are performed with a reactive force field to predict physical properties (gelation point, evolution of network, mass density, volumetric shrinkage) and mechanical properties (Bulk modulus, Shear modulus, Young's modulus, Poisson's ratio, Yield strength) as a function of crosslinking density. The MD modeling procedure is validated herein using experimental measurements of the modeled PBZ resin. The results of this study are used to provide a physical understanding of the zero-shrinkage phenomenon of PBZ. This information is also a critical input to future process modeling efforts for PBZ composites.