Mechanical behavior of beams under large rotations and displacements was investigated. Using co-rotational approach given by Crisfield, three-dimensional beam finite element was modeled in Mathematica environment. The yielding non-linear equation system was solved by utilizing Newton-Raphson technique. Dynamic balance equations and numerical time int egration method were introduced, while the solution process was left for a future work. Comparisons with the results of ANSYS and other works in the literature are accomplished.