Reconstruction of indoor surfaces with limited texture information or with repeated textures, a situation common in walls and ceilings, may be difficult with a monocular Structure from Motion system. We propose a Semantic Room Wireframe Detection task to predict a Semantic Wireframe from a single perspective image. Such predictions may be used with shape priors to estimate the Room Layout and aid reconstruction. To train and test the proposed algorithm we create a new set of annotations from the simulated Structured3D dataset. We show qualitatively that the SRW-Net handles complex room geometries better than previous Room Layout Estimation algorithms while quantitatively out-performing the baseline in non-semantic Wireframe Detection.