Cyberbullying on the Twitter social media platform has emerged as a significant social problem in Indonesia, with adverse effects on the mental health and well-being of its victims. Given the enormous volume of daily tweets, automated detection of cyberbullying expressions has become an urgent necessity. This study aims to compare the performance of four kernel functions in the Support Vector Machine (SVM) algorithm namely Linear, Radial Basis Function (RBF), Polynomial, and Sigmoid for cyberbullying classification on Indonesian-language tweets. The dataset used is a publicly available corpus of 13,169 annotated tweets released by Ibrohim and Budi in 2019. The preprocessing pipeline includes case folding, text cleaning, slang normalization using a colloquial dictionary, stopword removal, and stemming based on the Sastrawi library. Text features are extracted using Term Frequency–Inverse Document Frequency (TF-IDF) with a combination of unigrams and bigrams limited to the top 5,000 features. Model training is conducted on a stratified 80:20 split. Experimental results show that the RBF kernel achieves the highest performance with an accuracy of 0.8281 and an F1-score of 0.8269, slightly outperforming the Linear kernel (accuracy 0.8258; F1-score 0.8256). The Sigmoid kernel reaches an accuracy of 0.8204, while the Polynomial kernel records the lowest performance (accuracy 0.7674). The Linear kernel proves to be the most efficient option with the shortest training time (9.19 seconds) without significantly compromising accuracy. These findings can support the development of automated content moderation systems on Indonesian-language platforms.