Lei Heng was from Yuncheng Prefecture, and served the government as a constable head. He stood at about 7 feet, with a purplish face, and a string of whiskers around his face. He possessed immense strength, and had the ability to jump across a body of water 3-4 metres wide, thus he earned his nickname. Lei was initially a blacksmith, later he became a butcher. He stood up to injustice, he was quite narrow-hearted. Lei excelled in martial arts and could jump across rivers, over walls with ease.
Once, Lei arrested Liu Tang, who had fallen asleep in a temple after drinking heavily, thinking that Liu was some wanted criminal. Lei went to Chao Gai's village for a rest, and Chao rescued Liu by lying to Lei that Liu was his nephew. Lei then released Liu Tang, but Liu was unhappy with Lei and caught up with him after he had left. Lei and Liu fought for many rounds, but neither emerged the winner. In the end, the fight was stopped by Chao Gai and Wu Yong.
After Chao Gai and his friends had robbed the convoy of birthday gifts, Lei and his companion Zhu Tong were assigned to arrest Chao and company. Zhu Tong ordered Lei to enter through the front door. Lei made loud noises on purpose to attract Chao Gai's attention, so Chao and his friends escaped easily.
Then, Lei Heng went to watch a performance, but forgot to bring any money with him. The singer Bai Xiuying kept pestering Lei to pay up, which angered Lei and he hit Bai's father in anger. Bai Xiuying and her father were close of friends of the magistrate, and so Lei was arrested. He was locked in chains and made to stand in front of a gate. Lei Heng's mother came to give him his meals, but had a quarrel with Bai Xiuying and Bai slapped Lei's mother. Lei Heng was a filial son and could not tolerate Bai's attitude towards his mother. He killed Bai Xiuying in anger.
Then, Lei was exiled to Jizhou, and Zhu Tong was the guard to escort him there. Zhu Tong was Lei's good friend and could not bear to see his friend suffer. Zhu released Lei Heng and went back, willing to accept punishment for allowing the criminal to escape. Lei brought his mother to Liangshan with him upon release.
Lei Heng became one of the leaders of the Liangshan infantry and 36 Heavenly Chieftains. He followed the Liangshan heroes on their campaigns against the Liao Tartars and southern rebels. During the Fang La campaign, Lei was assigned to attack Deqing Prefecture. He was killed by Si Xingfang in battle.