his research presents an optimum design method of partaiy prestressed beamu which satisfy the utimate strength cntena. serviceability criteria recommended by Building Code (ACI 318 00) and the minimum cost smutaneouuy The aougn aigorrim based or Partial Prestressing Ratio (PPR concept suggested by Naaman and snaakson is used process whie the Simplex Methodis used n the optmzaton