We develop a simple analytical model to estimate the thickness of a smoke layer formed by a plume of a large area fire and to account for crosswinds. We take advantage of the dominant flow features in the upper part of the rising plume and in the smoke layer far from the plume to model the transition of a vertical flow to a horizontally spread thin smoke (or dust) layer. A one-dimensional approximation is used to model the buoyancy decay and plume overshoot. That solution is matched and combined with a solution based on the work required to establish our asymptotic horizontal smoke layer. The solution estimates the thickness of the spreading smoke layer. The solution estimates the thickness of the spreading smoke layer in a quiescent atmosphere or in an ambient wind field.