Friction welding of titanium and aluminium is numerically modeled by the axisymmetric thermal elastic-plastic analysis. In titanium/aluminium friction welding, heat transfers into the titanium substrate to a distance of z=10(mm) on the side of the bondline and into the whole region of the aluminium substrate having the large thermal conductivity. Adjacent to the bondline, $^{sigma}r;and;^{sigma heta}$ are tensile in the substrate whose thermal shrinkage is large, and are compressive in the substrate whose thermal shrinkage is small. $sigma_z$ along the radial direction is large tensile at the periphery of the component. Plastic strain occurs only close to the bondline in the aluminium substrate. In the components of plastic strain, $varepsilon^p_r;and;varepsilon^p_{ heta}$ have positive values and $varepsilon^p_r$ has large negative value. However, $varepsilon^p_r$ is produced not because of the severity of the mechanical restraint condition, but on purpose to satisfy the condition of the volume constant. A plastic work is proposed as a measure to evaluate the mechanical severity. The plastic work is larger in the aluminium substrate than that in the titanium substrate. The mechanical condition is severer in the aluminium substrate.