Automatic transmission control apparatus and method

During control of a shift of a first friction engagement element from an engaged state into a disengaged state and a shift of a second friction engagement element from a disengaged state into an engaged state for a gear shift to a first target gear from a second target gear, a desired torque capacity of the first friction engagement element is set based on an actual transmission gear ratio by interpolation from values of the desired torque capacity corresponding to at least first and second reference transmission gear ratios, wherein the first reference transmission gear ratio is a transmission gear ratio at start of an inertia phase of the shift control. When the first reference transmission gear ratio is between the actual transmission gear ratio and the second reference transmission gear ratio, the desired torque capacity is set to the value corresponding to the first reference transmission gear ratio.