This paper generalizes the actuator disc theory to the application of crosswind kite power systems. For simplicity, it is assumed that the kite sweeps an annulus in the air, perpendicular to the wind direction (i.e. straight downwind configuration with tether parallel to the wind). It is further assumed that the wind flow has a uniform distribution. Expressions for power harvested by the kite is obtained, where the effect of the kite on slowing down the wind (i.e. the induction factor) is taken into account. It is shown that although the induction factor may be small for a crosswind kite (of the order of a few percentage points), neglecting it in calculations may result in noticeable overestimation of the amount of power harvestable by a crosswind kite system.