Accurate estimation of rock elastic and failure parameters plays a vital role in the petroleum, civil, and geotechnical engineering applications. During drilling operations, continuous logs of rock elastic and failure parameters are considered very helpful to optimize geomechanical earth models. Commonly, rock elastic and failure parameters are estimated using well logs and empirical correlations. These are calibrated with rock mechanics laboratory experiments conducted on core samples. However, since these samples are expensive to get and time-consuming to test. Artificial Intelligence (AI) models based on available petrophysical well logs such as bulk density, compressional wave travel time, and shear wave travel time are utilized to predict static Young's modulus (Estatic) and unconfined compressive strength (UCS) – with an emphasis on carbonate rocks. We present two AI techniques in this study: artificial neural network (ANN) and adaptive neuro fuzzy inference system (ANFIS). The dataset used in this study contains 120 data points obtained from a Middle Eastern carbonate reservoir from which we develop an empirically correlated ANN model to predict Estatic and ANFIS model to predict UCS. A comparison between the UCS, predicted by the proposed ANFIS model, and with the published correlations show that ANFIS model predicted the UCS with less error and high coefficient of determination. The error obtained from ANFIS model was 4.5% while other correlations resulted in up to 30% of error on a published dataset. On the basis of results obtained we can say that the developed models will help geomechanical engineers to predict Estatic and UCS using well logs without the need to measure them in the laboratory.