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We model the present day, observable, normal radio pulsar population of the Small Magellanic Cloud (SMC). The pulsars are generated with SeBa, a binary population synthesis code that evolves binaries and the constituent stellar objects up to remnant formation and beyond. We define radio pulsars by selecting neutron stars that satisfy a selection of criteria defined by Galactic pulsars, and apply the detection thresholds of previous and future SMC pulsar surveys.The number of synthesised and recovered pulsars are exceptionally sensitive to the assumed star formation history and applied radio luminosity model, but is not affected extensively by the assumed common envelope model, metallicity, and neutron star kick velocity distribution. We estimate that the SMC formed (1.6$\pm$0.3)$\times 10^4$ normal pulsars during the last 100 Myrs. We study which pulsars could have been observed by the Parkes multibeam survey of the SMC, by applying the survey's specific selection effects, and recover 4.0$\pm$0.8 synthetic pulsars.This is in agreement with their five observed pulsars. We also apply a proposed MeerKAT configuration for the upcoming SMC survey, and predict that the MeerKAT survey will detect 17.2$\pm$2.5 pulsars.