A new model of plasma etch process was constructed by using a radial basis function network (RBFN). This technique was applied to an etching of silicon carbide films in a NF$_3$ inductively coupled plasma. Experimental data to train RBFN were systematically collected by means of a 2$^4$ full factorial experiment. Appropriateness of prediction models was tested with test data consisted of 16 experiments not pertaining to the training data. Prediction performance was optimized with variations in three training factors, the number of pattern units, width of radial basis function, and initial weight distribution between the pattern and output layers. The etch responses to model were an etch rate and a surface roughness measured by atomic force microscopy. Optimized models had the root mean-squared errors of 26.1 nm/min and 0.103 nm for the etch rate and surface roughness, respectively. Compared to statistical regression models, RBFN models demonstrated an improvement of more than 20 % and 50 % for the etch rate and surface roughness, respectively. It is therefore expected that RBFN can be effectively used to construct prediction models of plasma processes.