Recent applications of machine learning algorithms in the seismic domain have shown great potential in different areas such as seismic inversion and interpretation. However, such algorithms rarely enforce geophysical constraints — the lack of which might lead to undesirable results. To overcome this issue, we have developed a semisupervised sequence modeling framework based on recurrent neural networks for elastic impedance inversion from multiangle seismic data. Specifically, seismic traces and elastic impedance (EI) traces are modeled as a time series. Then, a neural-network-based inversion model comprising convolutional and recurrent neural layers is used to invert seismic data for EI. The proposed workflow uses well-log data to guide the inversion. In addition, it uses seismic forward modeling to regularize the training and to serve as a geophysical constraint for the inversion. The proposed workflow achieves an average correlation of 98% between the estimated and target EI using 10 well logs for training on a synthetic data set.