Despite technological advancements, ensuring aircraft safety remains a challenge, however, Machine learning (ML)-based approaches for predicting future incidents play a crucial role in addressing flight safety. As ML models increase in complexity, their decision-making process becomes less transparent, posing significant challenges to trustworthiness. While simpler models demonstrate lower accuracy, more intricate models such as deep neural networks achieve higher accuracy but sacrifice interpretability. In this study, we enhance trustworthiness in aircraft safety prediction by leveraging a dataset of past accidents and incidents to prevent similar accidents from occurring in the future. To achieve this, we apply Random Forest and Extreme Gradient Boosting models to classify different categories of aircraft incidents. Additionally, we apply two powerful explainable artificial intelligence (XAI) techniques: Local Interpretable Model-Agnostic Explanations (LIME) and Shapley Additive exPlanations (SHAP) to provide insights into both local and global predictions made by the models. Notably, our results reveal high accuracy in these predictions while maintaining trustworthiness. This research contributes to the advancement of XAI and offers valuable insights for safety-critical applications and decision support systems.