Phloem transport is the process by which plants internally distribute assimilates. The loading of assimilates near the photosynthetic source is responsible for generating enough osmotic pressure to drive sap flow towards the sink tissues where assimilates are consumed. Phloem loading is variable and subject to a diurnal cycle. It is dominated by photosynthesis during the day and by degradation of leaf starch to sugars at night. Most studies ignore the effect of the loading cycle on transport and assume that sugar flow operates at equilibrium. In this study, phloem transport was simulated for three successive days using a finite element model of time-dependent Münch-Horwitz equations. The spatial and temporal distributions of phloem pressure, sucrose concentration, sap velocity and sucrose flux were predicted for five different time variations in sucrose loading. Results showed that periodic loading induces an alternance of two distinct transport phases: one with high pressure, concentration and sucrose flux magnitudes and another with low magnitudes. In contrast, phloem water velocity remained remarkably stable. The alternating phases persisted over time and, under source-driven variation, transport did not reach steady-state conditions for the tested configuration. However, the impact of loading dynamics on transport was mitigated by pathway effects. Oscillations were not only delayed as one travelled away from the source, their amplitude was also reduced over distance. That behaviour stabilized the supply of sucrose to the sink, which continued at moderate levels during the dark cycles. This finding suggests that transport would assist night conversion of starch to sugars in the leaf to prevent carbon starvation at distant sinks in the early morning. The propagation velocity of pressure/concentration waves in phloem was predicted to vary by a factor up to 2.5 depending on the time series chosen to describe the dynamics of loading. Finally, the model predicted that up to 87% of the amount of sucrose loaded over 48 h would be unloaded under time-dependent loading, whereas only 76% would under constant-rate loading. This additional efficiency was periodic. It did not increase significantly the overall efficiency of the system but could be responsible for inducing rhythms in sink activity.