  For a sperm cell-like flagellated swimmer in an unbounded domain, several
numerical models of different fidelity are considered based on the Stokes flow
approximation. The models include a Regularised Stokeslet Method and a 3D
Finite Element Method, which serve as the benchmark solutions for several
approximate models considered. The latter include the Resistive Force Theory
versions of Lighthill and Gray and Hancock as well as a simplified
approximation based on computing the hydrodynamic forces exerted on the head
and the flagellum separately. It is shown how none of the simplified models is
robust enough with regards to predicting the effect of the swimmer head shape
change on the swimmer dynamics. For a range of swimmer motions considered, the
resulting solutions for the swimmer force and velocities are analysed and the
applicability of the Stokes model for the swimmers in question is probed.
