The complexation of charged surfactant molecules and oppositely charged polyelectrolytes was studied by the use of a mean-field lattice theory for flexible polyelectrolytes and surfactants in solution. The effect on the critical aggregation concentration, cac, and the surfactant aggregation number, N-agg, of (i) salt concentration, (ii) polyelectrolyte concentration, (iii) linear charge density of the polyelectrolyte, and (iv) hydrophobicity of the polyelectrolyte was investigated. The changes in the cac and N-agg upon changes of polyelectrolyte properties were found to qualitatively agree with experimental results, but the predicted cac was slightly decreased at salt addition instead of being increased as experimentally observed. The results showed that the solvency of the polymer backbone affected the structure of the aggregate. A polyelectrolyte with a hydrophilic backbone was accumulated in the headgroup region and slightly outside it but did not otherwise penetrate the micelle. For the case with a hydrophobic backbone, a substantial penetration of the micellar core was found, which also was accompanied by a reduction of the cac and, at a low Linear charge density of the polyelectrolyte, a diminished aggregation number.