The knowledge of the distribution of local micromechanical fields is crucial in the design of composite materials. Traditionally finite element methods (FEM) are used to obtain the local fields. However, FEM simulations are computationally expensive. Recently, there is a push towards using the big-data-driven machine learning approaches to solve composite materials mechanics. In this thesis, we use one of the deep learning-based algorithms known as the convolutional neural network (CNN) to estimate the local strains fields in a two phase composite material. Six different classes, or morphological distribution of the second phase, and two volume fractions of 10% and 30% are considered. Hundred three dimensional Representative volume elements(RVEs) in each class and volume fraction are used, out of which fifty are used for training and the remaining for testing the CNN model. The results from the CNN model reveal that for a given morphology, predictions are better for lower volume fraction. Further, for a given volume fraction, the morphology of the phases decides error measure.