Spectra of KS0 mesons and Λ hyperons were measured in p + C interactions at 31 GeV/c with the large acceptance NA61/SHINE spectrometer at the CERN SPS. The data were collected with an isotropic graphite target with a thickness of 4% of a nuclear interaction length. Interaction cross sections, charged pion spectra, and charged kaon spectra were previously measured using the same data set. Results on KS0 and Λ production in p + C interactions serve as a reference for the understanding of the enhancement of strangeness production in nucleus-nucleus collisions. Moreover, they provide important input for the improvement of neutrino flux predictions for the T2K long baseline neutrino oscillation experiment in Japan. Inclusive production cross sections for KS0 and Λ are presented as a function of laboratory momentum in intervals of the laboratory polar angle covering the range from 0 up to 240 mrad. The results are compared with predictions of several hadron production models. The KS0 mean multiplicity in production processes 〈nKS0〉 and the inclusive cross section for KS0 production σKS0 were measured and amount to 0.127 ± 0.005 (stat) ± 0.022 (sys) and 29.0 ± 1.6 (stat) ± 5.0 (sys) mb, respectively. © 2014 American Physical Society.