The TullyFisher (TF) relation links the stellar content of disk galaxies with their rotation velocity, being one of the most fundamental scaling relation for disk galaxies. We use the eagle cosmological simulation to study the stellarmass TF relation and its redshift evolution for the population of rotationallysupported galaxies with stellar mass Mstr > 10^9 Mo . We find a good agreement with available observations up to z = 1, which indicate no evolution in the slope and a weak decrease in the TF zero- point with redshift. Simulated galaxies have flat rotation curves but the relevance of the baryons depend on their mass. The slope of the TF is quite steep, Mstr ∝ Vhalf, where Vhalf is the circular velocity measured at rh . This steep slope can be explained by a simple model based on the scaling of virial quantities modulated by the varying efficiency of halos to collect baryons at their centers. The same model can also explain the weak evolution of the zeropoint, mainly as a result of a weaklyevolving relation between stellar mass and halo mass, which is consistent with arguments from abun- dance matching. We report predictions for the stellarmass TF relation up to z ∼2.2 that can be tested once unbiased observational data becomes available.