The thesis explores the application of deep reinforcement learning techniques to the task of motion planning of autonomous vehicles, where the data for training is generated by the vehicle executing actions through trial and error to learn a driving policy. The thesis work implements reinforcement learning algorithm called Soft-Actor Critic algorithm for motion planning in static environments and investigates the extension of the methodology to dynamic environments. The deep reinforcement learning framework is integrated in a driving simulator called CARLA, for training and testing. High dimensional action and state spaces inherent to autonomous vehicle motion planning, along with the requirement of large computational resources and training time, presents a challenge for applicability of the reinforcement learning framework. To ensure computational feasibility, given the available computational resources and reducing training times, a reduced action space is used. The thesis employs Soft-Actor Critic algorithm to learn the steering control for a fixed throttle value of the agent using the image from a front-facing camera on the ego vehicle as input, to solve the problem of motion planning in static environments.An extension of the method for dynamic environments can be to segregate the control into lateral control using pure-pursuit control and longitudinal control using the Soft-Actor Critic algorithm, among others.The observed results for various driving situations in the static environment demonstrate the ability to learn driving policies without pre-existing driving datasets. However, enhancements in diversity in training environment, better perception, hyper-parameter tuning of the policy and value networks, increased computational resources, and the integration of imitation learning can potentially lead to better results.