The ability to solve various constraints is a principal factor of automatic constraint solvers. Most object-oriented languages treat a character string as a primitive data type which is manipulated by string library functions. Most constraint solvers have limitations on their input constraints, such as strong restrictions on the expressiveness of constraints or lack of the ability to solve hybrid constraints. These limitations hinder applying automated constraint solvers on program analysis techniques for programs containing strings and string manipulation functions. We propose an approach to automatically solve program constraints involving strings and string manipulation functions. Based on the character array model, we design a constraint language which contains primitive operations to precisely describe the constraints of commonly used string manipulation functions. The translated string constraints together with numeric constraints are then solved by a two-phase test generation procedure: firstly, a partial solution is obtained to satisfy the arithmetic constraints of the position variables, and the solution is utilized to simplify the string constraints into pure character array constraints; secondly, the pure array constraints are solved by an off-the-shelf array-specific theory based constraint solver. We integrate the approach into an automated testing tool to support the generation of string test cases, and then perform experiments. The results of the experiments prove that the integration of the proposed approach promotes the testing coverage of the existing testing tool, and the integrated tool has an advantage of handling specific string manipulation functions compared with an existing string solver.