This paper explores the Built-In Self Test (BIST) concepts to test the configurable logic blocks (CLBs) of Static RAM (SRAM) based FPGAs using Java Bits (JBits). The proposed technique detects and diagnoses single and multiple stuck-at faults in the CLBs while significantly reducing the time taken to perform the testing. Previous BIST approaches for testing FPGAs use traditional CAD tools which lack control over configurable resources, resulting in the design being placed on the hardware in a different way than intended by the designer. In this paper, the design of the logic BIST architecture is done using JBits 2.8 software for Xilinx Virtex family of devices. The test requires seven configurations and two test sessions to test the CLBs. The time taken to generate the entire BIST logic in both the sessions is approximately 77 seconds as compared with several minutes to hours in traditional design flow.