The elastic moduli of ultrathin poly(styrene) (PS) and poly(methylmethacrylate) (PMMA) films of thickness ranging from 200 nm to 5 nm were investigated using a buckling-based metrology. Below 40 nm, the apparent modulus of the PS and PMMA films decreases dramatically, with an order of magnitude decrease compared to bulk values for the thinnest films measured. We can account for the observed decrease in apparent modulus by applying a composite model based on the film having a surface layer with a reduced modulus and of finite thickness. The observed decrease in the apparent modulus highlights issues in mechanical stability and robustness of sub-40 nm polymer films and features.