The mechanical properties of Co3(Al,W) with the L12 structure have been investigated both in single and polycrystalline forms. The values of all the three independent single-crystal elastic constants and polycrystalline elastic constants of Co3(Al,W) experimentally determined by resonance ultrasound spectroscopy at liquid helium temperature are 15~25% larger than those of Ni3(Al,Ta) but are considerably smaller than those previously calculated. When judged from the values of Poisson’s ratio, Cauchy pressure and ratio of shear modulus to bulk modulus (Gh/Bh), the ductility of Co3(Al,W) is expected to be sufficiently high. In the yield stress-temperature curve, a rapid decrease and an anomalous increase in yield stress is observed in the low and intermediate (1000-1100 K) temperature ranges, respectively. The former is concluded to be due to the solid-solution hardening effect while the latter is attributed to thermally activated cross-slip of APB-coupled a/2<110> superpartial dislocations from octahedral to cube slip planes.