For program languages, testing plays a crucial role in the software development cycle, enabling the detection of bugs, vulnerabilities, and other undesirable behaviors. To perform software testing, testers need to write code snippets that execute the program under test. Recently, researchers have recognized the potential of large language models (LLMs) in software testing. However, there remains a lack of fair comparisons between different LLMs in terms of test case generation capabilities.In this paper, we propose TestEval, a novel benchmark for test case generation with LLMs. We collect 210 Python programs from an online programming platform, LeetCode, and design three different tasks: overall coverage, targeted line/branch coverage, and targeted path coverage. We further evaluate 17 popular LLMs, including both commercial and open-source ones, on TestEval. We find that generating test cases to cover specific program lines/branches/paths is still challenging for current LLMs, indicating a lack of ability to comprehend program logic and execution paths.