Achieving minimum cost and time in reservoir drilling requires evaluating the effects of the drilling parameters on the penetration rate and constructing a drilling rate estimator model. Several drilling rate models have been presented using the drilling parameters. Among these, the Bourgoyne and Young (BY) model is widely utilized in order to estimate the penetration rate. This model relates several drilling parameters to the penetration rate. It possesses eight unknown constants. Bourgoyne and Young have suggested the multiple regression analysis method in order to define these constants. Using multiple regressions leads to physically meaningless and out of range constants. In this work, the Cuckoo Optimization Algorithm (COA) is utilized to determine the BY model coefficients. To achieve this goal, the corresponding data for two wells are collected from one of the oilfields located in SW of Iran. The BY model constants are determined individually for two formations in one of the wells. Then the determined constants are used to estimate the drilling rate of penetration in the other well having the same formations. To compare the results obtained for COA, first, the two mathematical methods including progressive stochastic and multiple regressions were implemented. Comparison between these methods indicated that COA yields more accurate and reliable results with respect to the others. In the following, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) as meta-heuristic algorithms were applied on the field data in order to determine BY model’s coefficients. Comparison between these methods showed that the COA has fast convergence rate and estimation error less than others.