The development of open-source, multilingual medical language models can benefit a wide, linguistically diverse audience from different regions. To promote this domain, we present contributions from the following: First, we construct a multilingual medical corpus, containing approximately 25.5B tokens encompassing 6 main languages, termed as MMedC, enabling auto-regressive domain adaptation for general LLMs; Second, to monitor the development of multilingual medical LLMs, we propose a multilingual medical multi-choice question-answering benchmark with rationale, termed as MMedBench; Third, we have assessed a number of open-source large language models (LLMs) on our benchmark, along with those further auto-regressive trained on MMedC. Our final model, MMed-Llama 3, with only 8B parameters, achieves superior performance compared to all other open-source models on both MMedBench and English benchmarks, even rivaling GPT-4. In conclusion, in this work, We present a large-scale corpus, a benchmark and a series of models to support the development of multilingual medical LLMs.