This article introduces a Random Survival Forest (RSF) method for functional data. The focus is specifically on defining a new functional data structure, the Censored Functional Data (CFD), for addressing the challenge of accurately modelling time-to-event data in the presence of censoring and irregular temporal structures. Traditional survival models struggle to incorporate complex functional patterns, making the proposed approach particularly valuable for improving prediction and interpretation. This approach allows for precise modelling of functional survival trajectories, leading to improved interpretation and prediction of survival dynamics across different groups. A medical survival study on the benchmark Sequential Organ Failure Assessment (SOFA) dataset and an extensive simulation study are presented. Results show good performance of the proposed approach, particularly in ranking the importance of predicting variables.