In this paper, we present three counterfeiting attacks on the block-wise dependent fragile watermarking schemes. We consider vulnerabilities such as the exploitation of a weak correlation among block-wise dependent watermarks to modify valid watermarked images, where they could still be verified as authentic, though they are actually not. Experimental results successfully demonstrate the practicability and consequences of the proposed attacks for some relevant schemes. The development of the proposed attack models can be used as a means to systematically examine the security levels of similar watermarking schemes.