Non-steady-state solidification of YBa2Cu3O6+δ (Y-123) superconducting oxides was observed by the isothermal undercooling experiment. A sudden decrease in crystal growth rate was found for all the Y-123 samples processed at the different temperatures and from the different Y2BaCuO5 (Y-211) contents in the initial composition. Quantitative analysis revealed that the Y-211 particles are pushed by the Y-123 crystal and accumulate in the liquid during solidification. It is also found that the particle volume fraction increased and reached a constant value of about 0.6, when the growth rate decreased abruptly, regardless of a variety of growth conditions. A simple solidification model is developed to interpret the experimental observation. This model shows that particle accumulation, as a result of the particle-pushing behavior, causes less connectivity of the liquid and thereby decreases the liquid diffusion flux, which is responsible for the non-steady-state solidification of Y-123.