A search for KS(L)0→μ+μ-μ+μ- decays is performed using proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.1  fb-1. No evidence for signal is found. The 90% confidence level upper limits are the first set for both decays and are B(KS0→μ+μ-μ+μ-)<5.1×10-12 and B(KL0→μ+μ-μ+μ-)<2.3×10-9.