Conventional Cobb-Douglas and Transcendental Logarithmic production functions widely used in Stochastic Production Frontier Estimation and Inefficiency Analysis have merits and deficiencies. The Cobb-Douglas function imposes monotonicity and concavity constraints required by microeconomic theory. However it is inflexible and implies undesired assumptions as well. The Trans-log function is very flexible and does not imply undesired assumptions, yet it is very hard to impose both monotonicity and concavity constraints. The first essay introduced a class of stochastic production frontier estimation models that impose monotonicity and concavity constraints and suggested models that are very flexible. Researchers can use arbitrary order of polynomial functions or any function of independent variables within the suggested frameworks. Also shown was that adopting suggested models could greatly increase predictive accuracy through simulations. In the second essay we generalized the suggested models with the Inefficiency Analysis technique. In the last essay we extended the models developed in the previous two essays with regression spline and let the data decide how flexible or complicated the model should be. We showed the improvement of deterministic frontier estimation this extension could bring through simulations, as well. Works in this dissertation reduced the gap between conventional structural models and nonparametric models in stochastic frontier estimation field. This dissertation offered applied researchers Stochastic Production Frontier models that are more accurate and flexible than previous ones. It also preserves constraints of economic theory.