An efficient combination of ADM and the Sumudu transformation for solving random ordinary differential equations (RODEs) is introduced as a novel tool to obtain an accurate analytical solution. It is an elegant combination of ST-ADM. The suggested method will convert differential equations into iterative algebraic equations, thereby reducing computational and analytical effort. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using several numerical examples, and the findings demonstrate that it is easier to use than many other numerical methods. It has also been established that (STADM) is a trustworthy technique for solving differential equations. Using the Mathematica 13.3 program. Applications are presented as examples of how the proposed technique can be used to obtain analytical or numerical solutions to certain kinds of Random Differential Equations (RODEs), thereby demonstrating its efficacy and potential.