© 2019, The Author(s). The first untagged decay-time-integrated amplitude analysis of Bs0 → KS0K±π∓ decays is performed using a sample corresponding to 3.0 fb−1 of pp collision data recorded with the LHCb detector during 2011 and 2012. The data are described with an amplitude model that contains contributions from the intermediate resonances K*(892)0,+, K2*(1430)0,+ and K0*(1430)0,+, and their charge conjugates. Measurements of the branching fractions of the decay modes Bs0 → K*(892)±K∓ and Bs0→K*(—)(892)0K0(—) are in agreement with, and more precise than, previous results. The decays Bs0 → K0*(1430)±K∓ and Bs0→K0*(—)(1430)0K0(—) are observed for the first time, each with significance over 10 standard deviations.