Abstract Objective To examine the effects of health-related food taxes on substitution and complementary purchases within food groups, including from unhealthier to healthier alternatives and between brands. Methods We used data from a virtual supermarket experiment with data from 4,259 shopping events linked to varying price sets. Substitution or complementary effects within six frequently purchased food categories were analyzed. Products’ own- and cross-price elasticities were analyzed using Almost Ideal Demand System models. Results Overall, 37.5% of cross-price elasticities were significant (p < 0.05) and included values greater than 0.10. Supplementary and complementary effects were particularly found in the dairy, meats and snacks categories. For example, a 1% increase in the price of high saturated fat dairy was associated with a 0.18% (SE 0.06%) increase in purchases of low saturated fat dairy. For name- and home-brand products, significant substitution effects were found in 50% (n = 3) of cases, but only in one case this was above the 0.10 threshold. Conclusions/policy implications Given the relatively low own-price elasticities and the limited substitution and complementary effects, relatively high taxes are needed to substantively increase healthy food purchases at the population level. Trial registration This study included secondary analyses; the original trial was registered in the Australian New Zealand Clinical Trials Registry ACTRN12616000122459.