The yields of $$K^0_S$$mesons have been measured in inelastic p+p interactions at incident projectile momenta of 31, 40 and 80 $$\text {Ge}\hspace{-1.00006pt}\text {V}\!/\!c$$($$\sqrt{s_{NN}}=7.7, 8.8$$and 12.3 $$\text {Ge}\hspace{-1.00006pt}\text {V}$$, respectively). The data were recorded by the NA61$$/$$SHINE spectrometer at the CERN Super Proton Synchrotron and the $$K^0_S$$mesons identified via their decays into $$\pi ^{+} \pi ^{-}$$pairs. Double-differential distributions are presented as function of transverse momentum and rapidity. The mean multiplicities of $$K^0_S$$mesons were determined to be $$(5.95 \pm 0.19 (stat) \pm 0.30 (sys)) \times 10^{-2}$$at 31 $$\text {Ge}\hspace{-1.00006pt}\text {V}\!/\!c$$, $$(7.61 \pm 0.13 (stat) \pm 0.43 (sys)) \times 10^{-2}$$at 40 $$\text {Ge}\hspace{-1.00006pt}\text {V}\!/\!c$$and $$(11.58 \pm 0.12 (stat) \pm 0.55 (sys)) \times 10^{-2}$$at 80 $$\text {Ge}\hspace{-1.00006pt}\text {V}\!/\!c$$. The results on $$K^{0}_{S}$$production are compared with the production of charged kaons in corresponding reactions and with model calculations (Epos1.99, SMASH 2.0 and PHSD) as well as with published data from other experiments.