Randoop is a well-known tool that proposes a feedback-directed algorithm for automatic and random generation of unit tests for a given Java class. It automatically generates two test suites for the class under test: (1) an error-revealing test suite, and (2) a regression test suite. Despite successful experiences with applying Randoop on real world projects like Java Development Kit (JDK) which have led to creation of error-revealing tests and identification of real bugs, it has not been investigated in the literature how useful are the regression test suites generated by Randoop. In this paper, we have investigated flakiness and fragility of Randoop’s regression tests during evolution of 5 open source Java projects with a total of 78 versions. The results demonstrate that the flakiness of the regression tests is not generally noticeable, since in our dataset, only 5% of the classes have at least one flaky regression tests. In addition, test fragility analysis reveals that in most versions of the projects under study, the regression tests generated by Randoop could be successfully executed on many of later versions. Actually, for 2 out of 5 projects in the experiments, the regression tests generated for each version could be successfully executed on all the later versions of the project.