High-frequency sinusoidal oscillations of a coarse-grained polymer model are used to calculate the local dynamic mechanical properties (DMPs) of free-standing polymer thin films. The storage modulus G(') and loss modulus G(") are examined as a function of position normal to the free surfaces. It is found that mechanically soft layers arise near the free surfaces of glassy thin films, and that their thickness becomes comparable to the entire film thickness as the temperature approaches the glass transition T(g). As a result, the overall stiffness of glassy thin films decreases with film thickness. It is also shown that two regions coexist in thin films just at the bulk T(g); a melt-like region (G(')<G(")) near the free surfaces and a glass-like region (G(')>G(")) in the middle of the film. Our findings on the existence of a heterogeneous distribution of DMPs in free-standing polymer thin films provide insights into recent experimental measurements of the mechanical properties of glassy polymer thin films.