The orthorhombic Tm3+:YAlO3 crystal is promising for laser operation at the H43→F43 (1.5 μm) and H43→H53 (2.3 μm) transitions. Stimulated-emission cross-sections for these transitions are determined with polarized light. Peak values of 0.59×10-20 cm2 and 0.80×10-20 cm2 are found at 1438 nm and 2275 nm, respectively, both for E∥b. The cross-relaxation defining the upper-laser level lifetime is quantified. Continuous-wave lasing at the H43→H53 transition is achieved with an a-cut 1.5 at.% Tm:YAlO3 crystal. The laser generated 254 mW at 2273 nm with a slope efficiency of 17.8% and linear polarization (E∥b).