In this study, we report on the compressive behavior of Ti3AlC2 and Ti3Al0.8Sn0.2C2 MAX phases at room temperature. We found that these two phases could be classified as Kinking Nonlinear Elastic (KNE) solids. The cyclic compressive stressstrain loops for Ti3AlC2 and Ti3Al0.8Sn0.2C2 are typical hysteretic and fully reversible. At failure, both compositions fracture in shear with maximum stresses of 545MPa for Ti3AlC2 and 839MPa for Ti3Al0.8Sn0.2C2. Consequently, the macroshear stresses for failure, c, are 185MPa and 242MPa for Ti3AlC2 and Ti3Al0.8Sn0.2C2, respectively. In addition to the grain size effects, the presence of a ductile TixAly intermetallic distributed in the grain boundaries plays an important role in the enhancement of the ultimate compressive and macroshear stresses for Ti3Al0.8Sn0.2C2. SEM observations reveal that these two MAX phases exhibit crack deflections, intragranular fractures, kink band formation and delaminations, grain push-in and pull-out.