A method for model parameter identification as incorrect inverse problem solution has been proposed. Iterative regularization procedure and a numerical algorithm have been developed for the case of two-parameter models. The method has been tested in two cases concerning both linear and non-linear relationships between objective function and parameters. Random number generator has been employed for "experimental" data used in the parameter identification procedure. Initial approximation effects on both the identified parameters and the regularization parameter have been investigated. Statistical approach for the analysis of the model adequacy has been proposed. (c) 2004 Elsevier Ltd. All rights reserved.