The paper presents a finite element solver of 2D prismatic beam based on Timoshenko beam theory written in MATLAB. It corrects the conventional Euler-Bernoulli limitations with the introduction of shear deformation and moment of inertia, which makes it more dependable regarding thick, short or high-frequency beam cases. Many students usually work with black-box commercial tools like Femap or Ansys in classes and thus don’t know how things work under the hood. To tackle this, the entire process here is presented in a stepwise, clear and modular code. In that manner, students can observe each calculation and begin with developing their own engineering mindset and solutions. The solver takes input in the form of a spreadsheet, is user friendly and provides visual results of the undeformed and deformed shapes. It also calculates displacement, bending moments, shear force and stress contours to facilitate exploration with varied geometry, material, loads and boundary conditions and view the effect of each variable on the results. The value of the solver as an instructional tool is demonstrated when the solver results are compared to the commercial software results and experimental data. It is a useful guide for undergraduate classes on mechanics, finite element analysis, as well as computational modelling, and can be built upon as an educational platform in the future.