This paper concerns the problem of aircraft control during the takeoff roll in the presence of severe wind gusts. It is assumed that the aircraft moves on the runway with a constant axial acceleration from a stationary position up to a specific speed at which the aircraft can go into flight. The lateral motion is controlled by the steering wheel and the rudder and affected by side wind. The aim of control is to prevent rolling out of the aircraft from the runway strip. Additionally, the lateral deviation, lateral speed, yaw angle, and yaw rate should remain in certain thresholds during the whole takeoff roll. The problem is stated as a differential game with state constraints. A grid method for computing the value function and optimal feedback strategies for the control and disturbance is used. The paper deals both with a nonlinear and linearized models of an aircraft on the ground. Simulations of the trajectories are presented.