To predict the gain in a lasing transition in ions of a laser-produced plasma, it is essential to calculate the amount of the reabsorption of radiation emitted in the transition from the lower laser level to the ground state. An important quantity influencing the reabsorption is the plasma geometry as resulting from the design of the laser and target system. Modeling a nonaxially symmetrical geometry of the plasma arising from a target irradiated by line-focused laser beams, we consider the plasma in the form of a longitudinally cut-out circular cylinder, with central angle ø, and the length of the plasma much larger than its transversal extension. Accounting for the effect of resonance line trapping via the escape probability approach, and taking the absorption profile in the line center approximation, an explicit formula for the photon escape probability depending on the radial and angular coordinates of an interior point in the plasma is derived. This function is averaged over the angular variable to obtain an only radially varying mean escape probability.