This chapter extends the analytical applications of the CES production and cost functions of Arrow et al. (Rev Econ Stat 43:225–250, 1961), Uzawa (Rev Econ Stud 29:291–299, 1962), to Generalized CES functions—called the GCES production function and GCESC cost function. The GCES functions are the natural parametric extension of CES to give flexible substitution properties on the global domain with many factors. GCES can conveniently be used in specifying Computable General Equilibrium (CGE) multi-sector growth models with a production (technology, cost) side using many inputs (durable factors, intermediate inputs). The substitution elasticities are no longer restricted to be the same for preserving global concavity of the multi-factor functions. Explicit calculations of the Allen-Uzawa Partial Substitution elasticities ( \(\sigma _{ij}\) ) and the Hicks Partial Complementarity elasticities ( \(c_{ij}\) ) are instrumental in demonstrating economic implications of the parameters of GCES with global regularity and flexibility in the factor demand/inverse demand systems.