Membrane mechanical elastic properties regulate a variety of cellular processes involving local membrane deformation, such as ion channel function and vesicle fusion. In this work, we used molecular dynamics simulations to estimate the local elastic properties of a membrane. For this, we calculated the energy needed to extract a DOPE lipid molecule, modified with a linker chain, from a POPC bilayer membrane using the umbrella sampling technique. Although the extraction energy entails several contributions related not only to elastic deformation but also to solvation, careful analysis of the potential of mean force (PMF) allowed us to dissect the elastic contribution. With this information, we calculated an effective linear spring constant of 44 +/- 4 kJ.nm-2.mol-1 for the DOPC membrane, in agreement with experimental estimates. The membrane deformation profile was determined independently during the stretching process in molecular detail, allowing us to fit this profile to a previously proposed continuum elastic model. Through this approach, we calculated an effective membrane spring constant of 42 kJ-2.mol-1, which is in good agreement with the PMF calculation. Furthermore, the solvation energy we derived from the data is shown to match the solvation energy estimated from critical micelle formation constants. This methodology can be used to determine how changes in lipid composition or the presence of membrane modifiers can affect the elastic properties of a membrane at a local level.