Therapeutic resistance is a fundamental obstacle in cancer treatment. Tumors that initially respond to treatment may have a pre-existing resistant subclone or acquire resistance during treatment, making relapse theoretically inevitable. Here, we investigate treatment strategies that may delay relapse using mathematical modeling. We find that for a single-drug therapy, pulse treatment – short, elevated doses followed by a complete break from treatment – delays relapse compared to continuous treatment with the same total dose over a length of time. For tumors treated with more than one drug, continuous combination treatment is only sometimes better than sequential treatment, while pulsed combination treatment or simply alternating between the two therapies at defined intervals delay relapse the longest. These results are independent of the fitness cost or benefit of resistance, and are robust to noise. Machine-learning analysis of simulations shows that the initial tumor response and heterogeneity at the start of treatment suffice to determine the benefit of pulsed or alternating treatment strategies over continuous treatment. Analysis of 8 tumor burden trajectories of breast cancer patients treated at MSK shows the model can predict time to resistance using initial responses to treatment and estimated pre-existing resistant populations. The model calculated that pulse treatment would delay relapse in all 8 cases. Overall, our results support that pulsed treatments optimized by mathematical models could delay therapeutic resistance.