Understanding the mechanical properties of nanoconfined polymers is essential in the design of nanostructured soft materials. Here, we investigate the mechanical properties of free-standing polymer thin films by employing an atomistically based coarse-grained (CG) modeling approach. By examining three representative CG polymer models, i.e., polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(1-ethylcyclopentyl methacrylate) (PECPMA), our results show that the elastic moduli of nanoscale thin films are substantially reduced with decreasing film thickness compared to their bulk values at their glassy state. Specifically, the PS and PMMA films exhibit similar size-dependent elastic responses, and their film moduli are reduced compared to bulk values at a thickness of < 40 nm, which agrees well with previous experimental measurements. However, in a model methacrylate-based polymer useful in photolithography, PECPMA, the length scale where elastic modulus deviates from the bulk value is much larger (i.e., around 80 nm). The local molecular stiffness within the films assessed by the Debye-Waller factor further reveals a softer interfacial layer having a size of only a few nanometers. Based on our simulations, a bilayer composite model is employed to predict the elastic moduli of free-standing thin films, which uncovers the size scaling relationship that universally holds for all three polymers.