There is various methodologies and mathematical models developed to predict the steel fiber reinforced concrete strength (SFRC) and these methods are prominently used in their time. Due to enhancement in the technology new mathematical models are developed and compared them with the old ones, as per their fit and comparative betterment, these methods become significant for the use by the scientists, researchers and mathematicians. In the research paper discussed here has an objective to develop a new mathematical approach to predict the SFRC strength using two newly introduced models namely Artificial Neural Network Simulation (ANN) and Response surface methodology (RSM) to analyse Aspect ratio, Aggregate-cement ratio, Water-cement ratio, Percentage of fibre and Control strength (referred to as five pi terms). The comparison of these two methods with experimental strength shows the output for the best fit, the study further extended to compare between these two models with each other to find best fit out of these two models. The calculation of the influence of pi terms, mentioned above to predict the SFRC, make this study more fruitful.