The analysis of unilateral finlines has been completed using a new method, regular solution of singular integral equation (RSSIE). It is demonstrated that the results obtained by this method are more accurate than those computed by the spectral domain method (SDM) by comparing the data measured. In some special cases where the results can be obtained exactly, the new method gives more accurate values than those calculated by the SDM. Dominant and higher-order modes can be calculated effectively and accurately. The computer time required by this method is decreased considerably compared with SDM (about 1/45 of the time required by SDM).