Acceptance testing is a validation activity performed to ensure the conformance of software systems with respect to their functional requirements. In safety critical systems, it plays a crucial role since it is enforced by software standards. Test engineers need to identify all the representative test execution scenarios from requirements, determine the runtime conditions that trigger these scenarios, and finally provide the input data that satisfy these conditions. Given that requirements specifications are typically large and often provided in natural language, the generation of acceptance test cases tends to be expensive and error-prone. In this paper, we present UMTG, an approach that supports the generation of executable, system-level, acceptance test cases from requirements specifications in natural language, with the goal of reducing the manual effort required to generate test cases and ensuring requirements coverage. More specifically, UMTG automates the generation of acceptance test cases based on use case specifications and a domain model for the system under test, which are commonly produced in many development environments. Unlike existing approaches, it does not impose strong restrictions on the expressiveness of use case specifications. We rely on recent advances in natural language processing to automatically identify test scenarios and to generate formal constraints that capture conditions triggering the execution of the scenarios, thus enabling the generation of test data. In two industrial case studies, UMTG automatically and correctly translated 95% of the use case specification steps into formal constraints required for test data generation; furthermore, it generated test cases that exercise not only all the test scenarios manually implemented by experts, but also some critical scenarios not previously considered.