Depending on what type of problem you want to model, you will find simple FEA programs in BASIC (source code). I started using this tool with a PC program in BASIC, which I had to modify to admit more nodes (bigger Rigidity Matrix), and after that because my PC had 8 Kb of RAM only, to solve the damned matrix (Gauss-Jordan method), in a floppy disc.
So, if you want to know what you are doing I will recommend a similar approach in your learning process,