Polymers have been widely used as structural materials owing to their prominent mechanical properties, such as high strength per unit weight. One of the most attractive features of polymers as structural materials is the tunability of mechanical properties, which can vary significantly depending on molecular structure. For example, optimizing the spatial distribution and entanglement of polymer chains can lead to improved strength and toughness. Thus, elucidating the relationships between molecular structure and the mechanical properties is essential for the rational design of polymer materials. In this study, we performed coarse-grained molecular dynamics simulations of amorphous thermoplastic and thermosetting polymers, namely polycarbonate and epoxy, focusing on the effects of molecular structure on mechanical properties. For polycarbonate, we found that the strain-hardening modulus and chain extensibility are strongly influenced by spatial distribution but are relatively insensitive to polydispersity. This behavior is attributed to the higher rate of non-affine deformation in structures with a high radius of gyration. In contrast, maximum stress at fracture is significantly affected by both spatial distribution and polydispersity, owing to the enhanced ability to sustain entanglements at larger strains. For epoxy models based on bisphenol A diglycidyl ether with various cross-linking densities, we observed a pronounced effect of cross-linking on post-yield mechanical behavior. In addition, we demonstrate the applicability of machine-learning approaches for mapping molecular structural features to mechanical properties.