Fluid flows have been typically computed using the conventional computational fluid dynamics (CFD) approach, where discretized governing equations are solved on a grid using an iterative solver. Although this method has largely been successful in predicting a wide variety of flows, its application in flow control and large parametric studies is rather limited because of the involved computational costs. Recently, machine learning (ML) models, particularly deep learning algorithms, have become popular in data science but their applications in fluid flow computations are limited so far. This is primarily due to the requirement of huge training data as well as the blindness of the approach to the underlying flow physics. In this work, we explore the Physics-inspired Neural Network (PINN) model, which makes deep learning algorithms tractable to fluid flow computations, on classical benchmark problems. PINN while using most of the benefits of deep neural networks (DNN) also respects the flow physics and therefore is more amenable to generalization. Two classical problems-lid-driven cavity and flow past a cylinder—both in the incompressible laminar regimes are solved using the PINN approach using an ML code developed using the DeepXDE library. Results are compared with those obtained using iterative CFD solvers and good comparisons are obtained. Unlike the traditional CFD approach, no prior grids were necessary to compute the flows, and results were obtained almost instantly with different neuron distributions once the networks were trained. The study exhibits the potential of this approach in solving turbulent flows in complex configurations.