In a shift control device and a shift control method of a vehicular automatic transmission that performs a coast downshift by engagement switch between a release-side engagement element and an element-side engagement element at a time of deceleration of a vehicle, it is determined whether or not there is a driver's intention to decelerate the vehicle during the coast downshift. If an affirmative determination is made regarding the intention to decelerate the vehicle, the rise of engagement pressure of the engagement-side engagement element is stopped so as to cause the coast downshift not to progress. If a negative determination is made regarding the intention to decelerate the vehicle while the rise of the engagement pressure has been stopped, the engagement pressure of the engagement-side engagement element is raised again so as to cause the coast downshift to progress.