The principle of maximum likelihood is used to obtain estimates of the parameters in a regression model when the experimental observations are assumed to follow the Poisson distribution. The maximum likelihood estimates are shown to be equivalent to those obtained by minimization of a quadratic form which reduces to a modified chi square under the Poisson assumption. Computationally, both of these estimation procedures are equivalent to a properly weighted least squares analysis. Approximate tests of the assumed Poisson variation and “goodness of fit” of the data to the model are proposed. Applications of the estimation procedure to linear and nonlinear regression models are discussed, and numerical examples are presented.