Context. Software testing effort estimation is one of the important problems in software development and software testing life cycle. The object of the study is the process of estimating the agile testing efforts for small Web projects. The subject of the study is the multiple regression models for estimating the agile testing efforts for small Web projects. Objective. The goal of the work is the creation of the multiple non-linear regression model for estimating the agile testing efforts for small Web projects on the basis of the Johnson multivariate normalizing transformation. Method. The model, confidence and prediction intervals of multiple non-linear regression for estimating the agile testing efforts for small Web projects are constructed on the basis of the Johnson multivariate normalizing transformation for non-Gaussian data with the help of appropriate techniques. The techniques based on the multiple non-linear regression analysis using the multivariate normalizing transformations to build the models, equations, confidence and prediction intervals of multiple non-linear regressions are used. The techniques allow to take into account the correlation between random variables in the case of normalization of multivariate non-Gaussian data. In general, this leads to a reduction of the mean magnitude of relative error, the widths of the confidence and prediction intervals in comparison with the linear models and nonlinear models constructed using univariate normalizing transformations. Results. Comparison of the constructed model with the linear model and non-linear regression models based on the decimal logarithm and the Johnson univariate transformation has been performed. Conclusions. The multiple non-linear regression model to estimate the agile testing efforts for small Web projects is firstly constructed on the basis of the Johnson multivariate transformation for SB family. This model, in comparison with other regression models (both linear and non-linear), has a smaller value of the mean magnitude of relative error, smaller widths of the confidence and prediction intervals. The prospects for further research may include the application of other multivariate normalizing transformations and data sets to construct the multiple non-linear regression model for estimating the agile testing efforts for small Web projects.