To push or shove someone with one's elbow. He elbowed his way through the crowded room to get to the exit.
To make one's way by pushing with the elbows. She elbowed through the throng to reach the front of the line.
To displace or oust something or someone, especially gradually, as if by pushing with the elbows. Traditional bookshops are being elbowed out of business by online retailers.