An analytical method based on the boundary value technique is developed to study the systematic of symmetric as well as asymmetric wave-guide couplers. We have tested our model for symmetric and asymmetric couplers and our results are in good agreement with those of Takagi et al. Our technique is simple, straightforward with few mathematical simplifications and approximations. We obtain unique self-consistent single solution for the given guide geometry, therefore implying the mono-mode character of the waveguide coupler. Our formulism can predict the performance and the field characteristics of the coupler from the knowledge of the coupler geometry. Thus it may help in the design of diffused channel single mode rectangular core optical wave-guide couplers when adequate data is available.