A relatively new and large class of materials, two-dimensional (2D) early transition metal carbides (MXenes), produced by etching of A elements from their parent MAX phases, have demonstrated outstanding performance in many applications. However, the mechanical behavior of MXenes, which is critical for device fabrication and performance, has not been sufficiently investigated. In this work we report the results from in situ scanning electron microscopy (SEM) uniaxial compression experiments conducted on two types of multilayer accordion-like MXene particles, Ti2CTx and Ti3C2Tx, along both in-plane and out-of-plane directions. Significant anisotropic behavior was observed associated with progressive failure mechanisms. Molecular dynamics (MD) modeling was conducted to analyze the behavior of intact and defected monolayer Ti2C and Ti3C2 MXenes in tension and compression. Structural analysis for both in- and out-of-plane uniaxial compression is presented and compared with experimental data, revealing that the overall mechanism is controlled by the intrinsic elastic and plastic properties of MXenes, as well as their multilayer structures. The intrinsic material properties were estimated based on structural analysis from experimental results.