Slug test data obtained from tests performed in an unconfined aquifer are commonly analyzed by graphical or numerical approaches to determine the aquifer parameters. This paper derives three fourth-degree polynomials to represent the relationship between Bouwer and Rice's coefficients and the ratio of the screen length to the radius of the gravel envelope. A numerical approach using the nonlinear least squares and Newton's method is used to determine hydraulic conductivity from the best fit of the slug test data. The method of nonlinear least squares minimizes the sum of the squares of the differences between the predicted and observed water levels inside the well. With the polynomials, the hydraulic conductivity can be obtained by simply solving the nonlinear least squares equation by Newton's method. A computer code, SLUGBR, was developed from the derived polynomials using the proposed numerical approach. The results of analyzing two slug test datasets show that SLUGBR can determine hydraulic conductivity with very good accuracy.