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We present a novel framework to bootstrap Motion forecasting with Self-consistent Constraints (MISC). The motion forecasting task aims at predicting future trajectories of vehicles by incorporating spatial and temporal information from the past. A key design of MISC is the proposed Dual Consistency Constraints that regularize the predicted trajectories under spatial and temporal perturbation during training. Also, to model the multi-modality in motion forecasting, we design a novel self-ensembling scheme to obtain accurate teacher targets to enforce the self-constraints with multi-modality supervision. With explicit constraints from multiple teacher targets, we observe a clear improvement in the prediction performance. Extensive experiments on the Argoverse motion forecasting benchmark and Waymo Open Motion dataset show that MISC significantly outperforms the state-of-the-art methods. As the proposed strategies are general and can be easily incorporated into other motion forecasting approaches, we also demonstrate that our proposed scheme consistently improves the prediction performance of several existing methods.