In order to solve the dietary problems of patients with dysphagia, a mathematical model for predicting extrusion pressure is established. The predictive model parameters are determined with the aid of the finite element method, and a 3D printing nozzle capable of printing nutrient-rich sandwich food is designed according to the predictive model. Pumpkin puree and minced pork are verified according to IDDSI standards. Finally, the accuracy of the predictive model and the printing effect of the design nozzle are verified by extrusion and printing experiments, respectively. The results show that four groups of simulation experiments reveal that the extrusion pressure increases by 15.6%, 13.5%, 12.7% and 12.4%, respectively, with a 1 cm increase in nozzle length. When the nozzle length is in the range of 1–5 cm, the extrusion pressure increases with the increase of the volume flow rate in the extrusion cylinder. The extrusion speed has little correlation with the length of the nozzle outlet, but for every 1 cm³/s increase in the inlet volume flow rate, the extrusion speed increases by about 1.5%. The finite element simulation experiment determines that the parameters of the prediction model are σ₀ = 0.6, α = 1.1, m = 0.21, τ₀ = 0, β = 0.52 and n = 0.2; the error between the predictive value and the experimental value is 15%, and the printed sandwich food has smooth lines, good molding and complies with IDDSI standards.