In image compositing tasks, objects from different sources are put together to form a new image. Artists often increase realism by adding object shadows to match the scene geometry and lighting. However, creating realistic soft shadows requires skill and is time-consuming. We introduce a Soft Shadow Network to generate convincing soft shadows for 2D object cutouts automatically. SSN takes an object cutout mask as input and thus is agnostic to image types such as painting and vector art. Although inferring the 3D shape of an object from its silhouette can be ambiguous, it is easy for humans to get the 3D geometry from a 2D projection when it is in an iconic view. We follow this intuition and train the SSN to render soft shadows for objects' iconic views. To train our model, we design an efficient pipeline to produce diverse soft shadow training data using 3D object models. Our pipeline first computes a set of soft shadow bases by sampling hard shadows. During training, environment lighting maps that cover a wide spectrum of possible configurations are used to calculate the soft shadow ground truth using the shadow bases. This enables our model to see a complex lighting pattern and to learn the interaction between the lights and 3D geometries. In addition, we propose an inverse shadow map representation, which makes the training focused on the shadow area and leads to much faster convergence and better performance. We show that our model produces realistic soft shadow details for objects of different shapes. A user study shows that SSN generated shadows are often indistinguishable from shadows calculated by physics-based rendering. Our SSN can produce a shadow in real-time and it allows real-time interactive shadow manipulation. We develop a simple user interface and a second user study shows that amateur users can easily use our tool to generate soft shadows matching a reference shadow.