This work presents a proposal for controlling lateral and angular vibrations in the cabin of a high-speed elevator, considering the use of springs composed of shape memory alloy (SMA) and magnetorheological dampers. Numerical simulations are performed for a mathematical model with two degrees of freedom. For the passive system, lateral and rotational accelerations are analyzed for different travel speeds to determine passenger comfort levels for different speeds and to determine at which speeds the system has higher accelerations. To attenuate elevator vibrations, a magnetorheological damper parallel with the passive damper of the elevator rollers was considered, and the standard spring was replaced by a shape memory spring. A Linear Quadratic Regulator (LQR) control is proposed to control the damper force and spring stiffness. The numerical results demonstrated that the use of both the MR damper and the SMA spring was effective in reducing the acceleration levels of the elevator cabin, thus improving passenger comfort, as well as reducing the vibration levels of the elevator, and reducing the wear of the elevator’s mechanical and electronic components.