Open-source mathematical software has become an essential component of engineering education, scientific research, and industrial applications. Unlike proprietary software, open-source platforms provide free access to computational tools, enabling engineers, researchers, and students to perform numerical analysis, symbolic computation, optimization, simulation, visualization, and data analysis without licensing restrictions. Popular opensource mathematical software such as GNU Octave, Scilab, SageMath, Python (NumPy, SciPy, SymPy, Matplotlib), Maxima, and FreeMat have emerged as reliable alternatives to commercial packages like MATLAB, Mathematica, and Maple. This study evaluates the performance, usability, computational efficiency, functionality, documentation, community support, and engineering applicability of leading open-source mathematical software. A comparative evaluation framework based on engineering performance indicators is developed to analyze their suitability for various engineering disciplines. The findings indicate that Python-based scientific computing ecosystems provide the highest flexibility and scalability, while GNU Octave offers excellent compatibility with MATLAB. SageMath and Maxima demonstrate strong symbolic computation capabilities, whereas Scilab performs efficiently in numerical simulation and control system analysis. The study concludes that open-source mathematical software provides costeffective, scalable, and technically robust solutions for engineering education, research, and industrial problemsolving. Keywords: Open-Source Software, Engineering Mathematics, Scientific Computing, Numerical Analysis, Python, GNU Octave, Scilab, SageMath, Computational Engineering.