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A search for $K_{\textrm{S(L)}}^0\rightarrow\mu^{+}\mu^{-}\mu^{+}\mu^{-}$decays is performed using proton-proton collision data collected by the LHCbexperiment at a centre-of-mass energy of 13 TeV, corresponding to an integratedluminosity 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$B(K_{\textrm{S}}^0\rightarrow\mu^{+}\mu^{-}\mu^{+}\mu^{-}) < 5.1\times10^{-12}$ and $B(K_{\textrm{L}}^0\rightarrow\mu^{+}\mu^{-}\mu^{+}\mu^{-}) <2.3\times 10^{-9}$.

Search for $K^0_{\mathrm{S(L)}}\to\mu^+\mu^-\mu^+\mu^-$ decays at LHCb