Semantic role labeling (SRL), also known as shallow semantic parsing, is an important yet challenging task in NLP. Motivated by the close correlation between syntactic and semantic structures, traditional discrete-feature-based SRL approaches make heavy use of syntactic features. In contrast, deep-neural-network-based approaches usually encode the input sentence as a word sequence without considering the syntactic structures. In this work, we investigate several previous approaches for encoding syntactic trees, and make a thorough study on whether extra syntax-aware representations are beneficial for neural SRL models. Experiments on the benchmark CoNLL-2005 dataset show that syntax-aware SRL approaches can effectively improve performance over a strong baseline with external word representations from ELMo. With the extra syntax-aware representations, our approaches achieve new state-of-the-art 85.6 F1 (single model) and 86.6 F1 (ensemble) on the test data, outperforming the corresponding strong baselines with ELMo by 0.8 and 1.0, respectively. Detailed error analysis are conducted to gain more insights on the investigated approaches.