Multilayer slab waveguides have become known as basic device structure in integrated optics. Results of waveguide analysis are very usefull in then study of mode propagation characteristics in a slab waveguide. This project intends to create a numerical analysis program for this purpose. Program is based on an accurate method for determining the complex propagation constants of guided mode and leaky mode. The method is a combination of stack matrix theory, Cauchy theorem, Rombeg integration technique, Lehmer--Schur search and generalized Newton method. Application of program in performing an analysisfor lossless waveguides, lossy waveguides, coupled waveguides, exponential profile waveguides and semidonducator laser waveguides are presented. The results shows an excellent aggreement with several previously published results.