Multimodal survival analysis aims to combine heterogeneous data sources (e.g., clinical, imaging, text, genomics) to improve the prediction quality of survival outcomes. However, this task is particularly challenging due to high heterogeneity and noise across data sources, which vary in structure, distribution, and context. Additionally, the ground truth is often censored (uncertain) due to incomplete follow-up data. In this paper, we propose a novel evidential multimodal survival fusion model, EsurvFusion, designed to combine multimodal data at the decision level through an evidence-based decision fusion layer that jointly addresses both data and model uncertainty while incorporating modality-level reliability. Specifically, EsurvFusion first models unimodal data with newly introduced Gaussian random fuzzy numbers, producing unimodal survival predictions along with corresponding aleatoric and epistemic uncertainties. It then estimates modality-level reliability through a reliability discounting layer to correct the misleading impact of noisy data modalities. Finally, a multimodal evidence-based fusion layer is introduced to combine the discounted predictions to form a unified, interpretable multimodal survival analysis model, revealing each modality's influence based on the learned reliability coefficients. This is the first work that studies multimodal survival analysis with both uncertainty and reliability. Extensive experiments on four multimodal survival datasets demonstrate the effectiveness of our model in handling high heterogeneity data, establishing new state-of-the-art on several benchmarks.