Prediction of the production rate of the cutting dimensional stone process is crucial, especially when chain saw machines are used. The cutting dimensional rock process is generally a complex issue with numerous effective factors including variable and unreliable conditions of the rocks and cutting machines. The Group Method of Data Handling (GMDH) type of neural network and Radial Basis Function (RBF) neural network, as two kinds of the soft computing method, are powerful tools for identifying and assessing the unpredicted and uncertain conditions. Hence, this work aims to develop prediction models for estimating the production rate of chain saw machines using the RBF neural network and GMDH type of neural network, and then to compare the results obtained from the developed models based on the performance indices including value account for, root mean square error, and coefficient of determination. For this purpose, the parameters of 98 laboratory tests on 7 carbonate rocks are accurately investigated, and the production rate of each test is measured. Some operational characteristics of the machines, i.e. arm angle, chain speed, and machine speed, and also the three important physical and mechanical characteristics including uniaxial compressive strength, Los Angeles abrasion test, and Schmidt hammer (Sch) are considered as the input data, and another operational characteristic of the machines, i.e. production rate, is considered as the output dataset. The results obtained prove that the developed GMDH model is able to provide highly promising results in order to predict the production rate of chain saw machines based on the performance indices.