The concept of a perspective class of vehicles—the quantomobiles, which utilize thrust from a quantum engine—requires the creation of models for understanding and implementation. The quantomobile development concept presents key differences from the classical automobile: the ability to apply thrust directly to the vehicle frame, the absence of transmission and driving wheels, and the capability for vehicle lift. In the MatLab environment, a longitudinal near-ground motion model for the quantomobile was created, implementing vectored thrust turning in the pitch plane, along with examples that reveal the unique features of this motion. The model incorporates two-parameter thrust control: thrust magnitude and the inclination angle of its vector. The vertical thrust component reduces resistance to the motion of supporting wheels, allowing for the optimization of quantomobile motion parameters. The thrust backspacing enables two-way longitudinal maneuvering of the vehicle. Calculations of vehicle motion, all based on a hypothetical quantomobile model analogous to a lorry, have been carried out. These calculations, using the quantomobile longitudinal near-ground motion model, have successfully addressed the challenges of representing and quantitatively evaluating the parameters of longitudinal quantomobile motion under vectored thrust control.