Abstract In this study, we investigate analytically the generation of mass flux due to a torsional Alfvén pulse. We derive that the presence of torsional Alfvén waves, which have been observed in, e.g., photospheric magnetic bright points (MBPs), can result in vertical plasma motions. The formation of this mass flux may even be a viable contribution to the generation of chromospheric mass transport, playing potential roles in the form of localized lower solar atmospheric jets. This relationship is studied using a flux tube model, with the waves introduced at the lower boundary of the tube as a magnetic shear perturbation. Due to the nature of MBPs we simplify the model by using the zero-beta approximation for the plasma inside the tube. The analytical results are demonstrated by an example of the type of Alfvén wave perturbation that one might expect to observe, and comparison is made with properties of spicules known from observations. We find that field-aligned plasma flux is formed nonlinearly as a result of the Lorentz force generated by the perturbations, and could be consistent with jet formation, although the current model is not intended to determine the entire evolution of a jet. Critical discussion of the model follows, including suggestions for improvements and for high-resolution proposed observations in order to constrain the driving magnetic and velocity shear.