Threshold testing, which is an LSI testing method based on the acceptability of faults, is effective in yield enhancement of LSIs and selective hardening for LSI systems. In this paper, we propose test generation models for threshold test generation. Using the proposed models, we can efficiently identify acceptable faults and generate test patterns for unacceptable faults with a general test generation algorithm, i.e., without a test generation algorithm specialized for threshold testing. Experimental results show that our approach is, in practice, effective.