This work is devoted to the application of the random forest approach to QSAR analysis of aquatic toxicity of chemical compounds tested on Tetrahymena pyriformis. The simplex representation of the molecular structure approach implemented in HiT QSAR Software was used for descriptors generation on a two-dimensional level. Adequate models based on simplex descriptors and the RF statistical approach were obtained on a modeling set of 644 compounds. Model predictivity was validated on two external test sets of 339 and 110 compounds. The high impact of lipophilicity and polarizability of investigated compounds on toxicity was determined. It was shown that RF models were tolerant for insertion of irrelevant descriptors as well as for randomization of some part of toxicity values that were representing a "noise". The fast procedure of optimization of the number of trees in the random forest has been proposed. The discussed RF model had comparable or better statistical characteristics than the corresponding PLS or KNN models.