Compressive properties of electrospun fiber mats are reported for the first time. Mats of bisphenol-A polysulfone (PSU) and of poly(trimethyl hexamethylene terephthalamide) [PA 6(3)T] were electrospun and annealed over a range of temperatures spanning the glass transition temperature of each polymer. The data for applied stress versus mat solidity were found to be well-described by a power law of the form $$ \sigma_{\text{zz}} = kE\left( {\phi^{n} - \phi_{0}^{n} } \right) $$ , where $$ \sigma_{\text{zz}} $$ is the applied stress and ϕ is solidity, in accord with the analysis of Toll (Polym Eng Sci 38(8):1337, 2004). The values of n range from 3.2 to 6 for PSU and from 8.0 to 20 for PA 6(3)T. The lowest values in each case were exhibited by mats annealed near the glass transition temperature of the fiber material. The values of n are independent of fiber diameter. The higher values of n are attributed to fiber slippage via a mechanism analogous to that of work hardening of metals. The values of kE can vary by an order of magnitude and were difficult to determine precisely, due to the nature of the power law and the inhomogeneity of the mats. The compressibility of electrospun mats in response to an applied stress is sufficiently large that it cannot be neglected in applications where large pressures may be involved, such as filtration or membrane separations. In addition to the initial solidity of the mats, the material compressibility and the operating pressure relevant to the application are important to describe the structure of electrospun mats quantitatively under conditions of use.