Microtubules regulate signaling, trafficking, and cell mechanics, but the respective contribution of these functions to cell morphogenesis and migration in 3D matrices is unclear. Here, we report that the microtubule plus-end tracking protein (+TIP) SLAIN2, which suppresses catastrophes, is not required for 2D cell migration but is essential for mesenchymal cell invasion in 3D culture and in a mouse cancer model. We show that SLAIN2 inactivation does not affect Rho GTPase activity, trafficking, and focal adhesion formation. However, SLAIN2-dependent catastrophe inhibition determines microtubule resistance to compression and pseudopod elongation. Another +TIP, CLASP1, is also needed to form invasive pseudopods because it prevents catastrophes specifically at their tips. When microtubule growth persistence is reduced, inhibition of depolymerization is sufficient for pseudopod maintenance but not remodeling. We propose that catastrophe inhibition by SLAIN2 and CLASP1 supports mesenchymal cell shape in soft 3D matrices by enabling microtubules to perform a load-bearing function.