The mechanical properties, specific energy and drilling performance of the rocks are influenced by the anisotropy. The anisotropy of the rocks is due to the discontinuity or due to variations in the size, shape and position of mineral grains. Prediction of specific energy and rate of penetration of rotary drilling is an essential step in designing drilling projects and evaluating the time and drilling performance. The present study can be In the first section of this thesis, the specimen size effect on uniaxial compressive strength of 114 rock samples and 84 concrete specimens using specimen size effect models has been investigated. The results of this section indicated that the prediction of specimen size effect models depends on the preparation and anisotropy of the specimens. In the igneous rocks, outputs of the multi-fractal scaling model and the specimen size effect model using the fracture energy theory and in the sedimentary rocks, results of the specimen size effect model using the fracture energy theory exhibited a better correlation with the results of previous laboratory tests. Also, in the concrete specimens, in the small diameters, results of Hoek and Brown model and in the large diameters, outputs of the multi-fractal scaling model indicated a better correlation with the results of previous laboratory tests. The results of this section can be utilized to design engineering projects at different scales such as repositories of storing oil and gas, underground power plants and radioactive waste repositories. In the second section, the effect of anisotropy on penetration rate of 91 m coring drilling conducted in state of Wyoming has been studied. Also, a combination of two techniques of non-linear statistical and artificial neural networks was used to estimate coring drilling performance. The results of non-linear statistical analysis exhibited that the four parameters of brittleness, RQD, humidity and anisotropy index have better correlation with the rate of drilling penetration. However, the values of the determination coefficient of the non-linear statistical models were low. For this reason, non-linear statistical models were developed using multi-layer perceptron neural network technique by MATLAB software. The results of this section show that the neural network is a useful tool to minimize uncertainties encountered during drilling process. In the third section, using physical modelling and statistical methods, the effect of the grain size, the discontinuity angle and also the effect of the sample diameter on the mechanical properties, rate of penetration and the drilling specific energy was studied. Also, novel models were proposed to predict the performance and drilling specific energy. In order to directly measure of the drilling specific energy, the laboratory automatic coring machine was designed and manufactured to determine the instantaneous and average trust on the drilling bit and the drilling specific energy. In this section, using physical modelling, 10 concrete blocks, with dimensions of 50 cm × 50 cm × 50 cm, with three angles of 30, 45 and 60 degrees and three grain sizes 0-9.5 mm, 0-12.5 mm and 0-19 mm were manufactured. Concrete blocks with three diameters of 52, 76 and 102 mm and with length of 50 cm were drilled using laboratory automatic coring machine. The results of 86 m drilling (172 cores and 688 prepared specimens) and 124 servo-control uniaxial compressive tests showed that, by increasing the angle of discontinuity from 30 to 60 degrees, the trust on the bit and drilling specific energy increase and rate of drilling penetration, the uniaxial compressive strength and the elastic modulus decrease. Also, in the low diameters of drilling, the specific energy values calculated from the Teale, Moore and Wang equations have a good correlation with the values of actual measured specific energy. The results of sensitivity analysis exhibited that three parameters, RQD, brittleness and discontinuity angle have a significant effect on the drilling specific energy. The results of this study can be successfully used to estimate mechanical properties and to predict specific energy and coring drilling performance in different geological conditions.