The Sigma =5 and 13 (001) twist boundaries in Cu₃Au are studied using the constant-temperature, pressure and chemical potential difference Monte Carlo method. An N-body potential and bulk-like boundary conditions are utilized. The properties studied include the stoichiometry profile, the structure factor and the average strain of the atoms along (001). The two boundaries exhibit similar behaviour at different temperatures below the order-disorder transition. The average strain at the boundary is about 7% and diminishes rapidly, within three atomic layers. No noticeable segregation effects are observed, only a tendency of Au atoms to be depleted from the Sigma =13 boundary. Around the boundaries we find a region with lower order than the rest of the material. This region broadens as the transition temperature is approached, thus establishing the presence of wetting.