The recently developed class of nanoporous materials known as metal-organic frameworks (MOFs) is generating considerable interest because of their potential in sensing, storage, and chemical separations. In many applications, it is essential to understand their mechanical properties. We report the measurement of the elastic modulus of IRMOF-1 crystals using two different nanoindentation techniques. The reduced modulus from continuous stiffness measurements, calculated from the average single-crystal Young’s modulus $\left(E\right)$ of $2.7\pm 1.0\mathrm{GPa}$, is in good agreement with the value obtained from conventional quasistatic measurements. Permanent deformation without fracture has been observed directly after indentation. For comparison, we performed density functional theory (DFT) calculations of the elastic properties using both the local density approximation (LDA) and the generalized gradient approximation (GGA). The resulting, well-converged DFT value (LDA-GGA average) for $E$ is $21.6\pm 0.3\mathrm{GPa}$, with $C_{11}=0.28\pm 0.01\mathrm{GPa}$, $C_{12}=0.11\pm 0.01\mathrm{GPa}$, and $C_{44}=0.03\pm 0.02\mathrm{GPa}$. Correcting the measured modulus for the highly anisotropic elastic behavior predicted by DFT suggests an effective modulus for the (100) face of $7.9\mathrm{GPa}$. The DFT prediction is expected to be reliable here. Therefore, the lower measured Young’s modulus is most likely due to an interesting behavior during fractureless plastic deformation that occurs in these framework materials. Deformation or buckling in this nanoporous structure likely leads to structural changes at the lowest loads we can apply in the experiment. This appears to be a unique property of MOFs, where the elastic properties of the plastically deformed materials behave differently than those for more traditional nanoporous metals, ceramics, and polymers.