In this dissertation, a new numerical method for solving some problems on the semiinfinite domain is presented. The method is based upon the modified rational Bernoulli functions. These functions are first introduced. Operational matrices of derivative and product of modified rational Bernoulli functions are then derived and are utilized to reduce the solution of the equations to a system of algebraic equations. This method is used to solve the following problems: Lane-Emden type equations, Volterra’s population model, Blasius equation, and MHD Falkner-Skan equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.