This paper deals with transient stability analysis based on time domain simulation on vector processing. This approach requires the solution of a set of differential equations in conjunction of another set of algebraic equations. The solution of the algebraic equations has presented a scalar as sequential set of tasks, and the solution of these equations, on vector computers, has required much more investigations to speedup the simulations. Therefore, the main objective of this paper has been to present methods to solve the algebraic equations using vector processing. The results, using a GRAY computer, have shown that on-line transient stability assessment is feasible.