Performance issues of multi-tier Web Services have been studied extensively in recent years. Performance modeling and prediction under failure of multi-tier architectures, however, is not well addressed yet. We propose a novel model named Performance under Failure of Multi-tier Architecture, or PerFAMA in short, to address this issue. We first show that the multi-tier architecture with failure considerations is a product-form network, and then analyze and model the failure impact. By applying the PerFAMA model, we are able to predict the end-to-end response time of multi-tier Web Services under failures. We have simulated two representative Web Services architectures and various failure scenarios to verify the proposed PerFAMA model. The experimental results show that the proposed model works well and the prediction accuracy is up to 98%.