The paper analyzes the influence of spindle speed, feed rate and axial depth of cut on vibration acceleration in feed direction during peripheral milling of high-density polyethylene. Experimental research was planned and implemented using the response surface methodology in the Design-Expert software package. Based on the experimental results, a statistical analysis was performed and a mathematical model was developed to predict vibration acceleration. The research results showed that feed rate and axial depth of cut have a dominant influence on vibration acceleration, while the influence of spindle speed is less pronounced. A reduced quadratic mathematical model was developed to describe the dependence between process parameters and vibration acceleration in feed direction. Model diagnostics and validation results confirmed its adequacy and good predictive ability. The obtained results can serve as a basis for selecting process parameters in order to reduce vibrations and improve the stability of the peripheral milling of high-density polyethylene.