Ultrasound elastography images the elasticity of a biological tissue. Conventional algorithms for ultrasound elastography suffer from different noises severely compromising the quality of time-delay estimation. Calculation of time-delay estimation is a key component of strain estimation. However, time-delay estimation is analogous to optical flow estimation, a classical computer vision problem. Deep learning networks have reported recent success in optical flow estimation compared to the conventional techniques. Classical ultrasound elastography algorithms have been unable to provide a single solution to both commonly known issues of noise and computation time. Deep learning techniques have a bright prospect in addressing both issues. The goal of this thesis is to investigate whether optical flow estimation is translatable to ultrasound elastography as the core nature of both of these problems are analogous. In this thesis we aim to develop and train a robust deep neural network for ultrasound elastography. First, an efficient deep learning network trained for optical flow estimation is used for time-delay estimation. The initial time-delay estimation is further fine-tuned by optimizing a global cost function for generating high quality strain images. Simulation, phantom and clinical experiments show the robustness of the deep learning approach both quantitatively and qualitatively. Next, the weights of the deep learning network are fine-tuned using transfer learning technique for transferring the efficacy of optical flow estimation to time-delay estimation. The objective is to retain the robustness introduced by the deep learning network while enhancing the overall performance of the time-delay estimation in ultrasound elastography. Simulation and experimental phantom results show that the time-delay estimation has improved slightly after fine-tuning the weights using transfer learning