The solution of the modal equation of a planar optical waveguide is a cumbersome job and usually incident angle of successful modes is determined by a graphical solution. In this research work, we applied two computational intelligence methods: Particle Swarm Optimization (PSO) and Genetic algorithm (GA) in a segment-wise approach to solving the modal equation of the tangent function. The motivation for employing Computational Intelligence (CI) lies in its ability to optimize functions without requiring high-level mathematics or complex statistical models, as opposed to traditional analytical methods. This strategic use of computational intelligence significantly reduces the overall computational cost, more nature inspired and probabilistic, providing an efficient alternative. Particularly for functions with complex solutions, the utilization of computational intelligence or soft computing methods becomes imperative to obtain an approximate solution compared to classical numerical optimization methods like Newton-Raphson, bisection etc. that generally deterministic and aim to find the exact optimal solution. In terms of using probability (a core component of chosen algorithm’s searching mechanism) we can incorporate distributions that will enhance the performance. Therefore, while classical root-finding methods are computationally simpler for isolated cases, the use of PSO and GA is motivated by their global search capability, robustness to initialization, and ease of automation, which are advantageous in generalized or large-scale modal solution frameworks. The outcomes derived from both methods (PSO and GA) are meticulously compared with the results obtained through the traditional graphical solution. We have found accuracy of 99.95% for PSO and 99.87% for GA. Notably, the findings reveal a close correlation between the computational intelligence approaches and the graphical method offering a promising avenue for advancing the field with a more computationally feasible approach.