The mechanical properties of lipid monolayers and their responses to shear and compression stresses play an important role in processes such as breathing and eye blinking. We studied the mechanical properties of Langmuir monolayers of a model mixture, composed of an unsaturated lipid, 1-palmitoyl-2-oleoyl-sn-glycero-phosphoethanolamine (POPE), and a saturated lipid, 1,2-dipalmitoyl-sn-glycero-phosphocholine (DPPC). We performed isothermal compressions and sinusoidal shear deformations of these mixed monolayers. Also, the different phases were observed with Brewster angle microscopy. We found that the mechanical behavior is affected by the miscibility of both lipids. In the two-phase region, the compression elastic modulus increases with the amount of the LC phase but does not follow the predictions of a simple effective medium model. The discrepancies arise from the fact that, upon compression, the domains grow at a rate faster than the compression rate but not fast enough to reach thermodynamic equilibrium. Before reaching the LC phase, domain percolation is observed and compression and shear moduli become equal to those of the pure LC phase. Most of the monolayers behave as viscoelastic fluids at the frequencies investigated. A minimum in the compression modulus and shear viscosity was observed for mixtures close to equimolar composition, with the minimum being accompanied by a change in domain shapes.