In Model-Based Testing (MBT) area, Search-Based Software Testing (SBST) has been employed to generate test cases from the model of a system under test. However, many types of models have been used in MBT. If the type of a model has changed from one to another, all functions of a search technique must be reimplemented because the types of models are different even if the same search technique has been applied. It requires too much time and effort to implement the same algorithm over and over again. We propose a model-independent software framework for SBST, which can reduce redundant works. The framework provides a reusable common software platform to reduce time and effort. The software framework not only presents design patterns to find test cases for a target model but also reduces development time by using common functions provided in the framework. We show the effectiveness and efficiency of the proposed framework with two case studies. The framework improves the productivity by about 50% when changing the type of a model.