Recently, deep reasoning LLMs (e.g., OpenAI o1/o3 and DeepSeek-R1) have shown promising performance in various complex tasks. Free translation is an important and interesting task in the multilingual world, which requires going beyond word-for-word translation and taking cultural differences into account. This task is still under-explored in deep reasoning LLMs. In this paper, we introduce DeepTrans, a deep reasoning translation model that learns free translation via reinforcement learning. Specifically, we carefully build a reward model with pre-defined scoring criteria on both the translation results and the thought process. Given the source sentences, the reward model teaches the deep translation model how to think and free-translate them during reinforcement learning. In this way, training DeepTrans does not need any labeled translations, avoiding the human-intensive annotation or resource-intensive data synthesis. Experimental results show the effectiveness of DeepTrans. Using Qwen2.5-7B as the backbone, DeepTrans improves performance by 16.3% in literature translation, and outperforms strong deep reasoning baselines as well as baselines that are fine-tuned with synthesized data. Moreover, we summarize the failures and interesting findings during our RL exploration. We hope this work could inspire other researchers in free translation.