This book studies the dynamic model and simulation of a Half-Toroidal (HT) type Continuously Variable Unit (CVU) integrated into conventional powertrain. A simplified parametric model of a HT-CVU is constructed using FInite Element Method (FEM) in which the continuous variable variable speed unit is discretized into lumped masses, spring and damper elements. Linearized Finite Elements (FE) have been used to model the contacts between the toroids and rollers. The phenomenon of a slip and spin associated with the rolling-slipping contacts of the traction drives are modelled kinematically. All FE including the CVU model are integrated into the complete powertrain system. Stability analysis is carried out on the powertrain to understand the effect of damping in the tyres and damping within the HT-CVU on the stability of powertrain. Future investigations need to be carried out in order to understand in depth the fluid-metal interaction in the HT-CVU. This can be achieved by modelling in non-linear drag torque which would act on the HT-CVU.