We numerically study the drafting mechanisms between a dolphin mother and her calf swimming near the free surface. Formation locomotion between the cetacean mother-calf pair provides a way for the mother to assist the calf in its locomotion. Depending on the age and size of the calf, it swims at neonate, echelon, and infant positions. At each position, the effects of the calf’s size, swimming speed, proximity to the free surface and the formation pattern are investigated and the optimal configurations predicted by the model based on the swimming hydrodynamics are compared with previous observations. It is shown that the neonate position is the optimal formation for controlling the separation of the calf, and the echelon position is the most hydrodynamically efficient position in transferring the thrust force from the mother to the calf. The infant position, on the other hand, avoids the energy loss due to wave generation so that it improves the self-propulsion performance of an older calf.