SLIM is a lightweight block cipher proposed by Aboushosha et al. and it is designed for RFID systems. It features 32‐bit block and 80‐bit key size. In this paper, we search for impossible differential distinguishers and related‐key differential distinguishers on SLIM by applying the constraint programming (CP) model based on satisfiability and the Boolean satisfiability problem (SAT). Our findings have revealed impossible differential distinguishers up to 7 rounds. We also searched for related‐key differential up to 26 rounds and found an 18 rounds path inducing a distinguisher. Furthermore, we demonstrate that 9‐round SLIM is vulnerable to impossible differential attack. This attack requires chosen plaintexts, encryptions, and bytes of memory complexity. Although this result does not achieve the best attack on round‐reduced SLIM, this is the first finding using impossible differential attack. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.