In this work, we consider a 2-d fiber-reinforced matrix composite plate where the fiber and matrix are linear and elastic. Under the application of different loading and boundary conditions, local stress and strain fields are generated throughout the domain of the plate. The stress field is also a function of the mechanical properties of the matrix and the individual fibers as well as the geometrical features of the model, such as the spatial distribution of the fibers, the shape of the fibers, and the volume fraction of the fiber material in the plate. Finite element method (FEM) is a numerical method used to solve this problem, but it is computationally expensive. The goal of this work is to use convolutional neural networks (CNNs) to build a surrogate model for cheaper stress prediction in composite materials under different spatial distributions of the fibers. A CNN architecture is used to essentially map the spatial distribution of the fibers in the composite material to the corresponding stress field contours under the application of some load. The advantage of using a CNN architecture is its ability to capture location invariant attributes from the input feature maps that help in making accurate predictions of the stress field.