The aerodynamic derivatives governing the crosswind sensitivity of a vehicle are the coefficients of side force and yawing moment. Usually, these derivatives are measured in a wind tunnel under stationary conditions, but driving through a wind gust or a vehicle's wake is a transient process. Therefore, when the behavioral characteristics of a vehicle in a crosswind are calculated with the aid of a mathematical model, the effects of transient aerodynamics should not be neglected. An estimate of these effects is made on a simple model describing the flow past a moving vehicle. At first, side force and yawing moment in stationary conditions are calculated on the slender body theory, which is converted from aircraft aerodynamics to the aerodynamic of ground vehicles. A reasonable agreement with full-scale measurements seems to justify the application of the same theory to the calculation of the transient crosswind-gust factor. Dependent on the gradient of the crosswind, the vehicle suffers from remarkable additional forces and moments due to quasi-stationary and transient effects.