Elastic full waveform inversion can construct highresolution P-wave and S-wave velocity models in complex geological settings. However, several factors make the application of elastic FWI challenging. Elastic FWI is prone to the problem of cycle skipping phenomenon when low-frequency in the data are unavailable and the starting model is inaccurate. Multiparameter FWI also suffers from crosstalk issue due to coupling between different model parameters. We extend our physics guided deep convolutional autoencoder network to the problem of multiparameter elastic full waveform inversion. Our training is completely unsupervised. Our autoencoder which is composed of convolutional neural networks (CNNs) maps the multicomponent shot gathers to the target velocity models. The output from the network is given as input to partial differential equations which generate synthetic data. We compare the observed data against the synthetic data and then compute the misfit. We calculate the gradient of the misfit with respect to the model parameters and then use it to update the neural network weights. We note that the neural network generates velocity models that explains the observed data. We demonstrate that the network can introduces regularization in the inversion and overcome issues related to cycle skipping and parameter crosstalks. A toy model, the marmousi model and left part of the BP salt model are used to demonstrate the effectiveness of the proposed approach. Finally, we provide an explanation of the efficacy of the proposed approach by examining the nature of the loss landscape of neural networks based full waveform inversion.