Model editing is a technique that edits the large language models (LLMs) with updated knowledge to alleviate hallucinations without resource-intensive retraining. While current model editing methods can effectively modify a model’s behavior within a specific area of interest, they often overlook the potential unintended side effects on the general abilities of LLMs such as reasoning, natural language inference, and question answering. In this paper, we raise concerns that model editing’s improvements on factuality may come at the cost of a significant degradation of the model’s general abilities. We systematically analyze the side effects by evaluating four popular editing methods on three LLMs across eight representative tasks. Our extensive empirical experiments show that it is challenging for current editing methods to simultaneously improve factuality of LLMs and maintain their general abilities. Our analysis reveals that the side effects are caused by model editing altering the original model weights excessively, leading to overfitting to the edited facts. To mitigate this, a method named RECT is proposed to regularize the edit update weights by imposing constraints on their complexity based on the RElative Change in weighT. Evaluation results show that RECT can significantly mitigate the side effects of editing while still maintaining over 94% editing performance.