This paper presents computer simulations of HTHS capillary viscometer dynamics for non-newtonian oils. The main objectives are to promote a deeper understanding of HTHS capillary viscometry and to support, on a theoretical basis, the empirical procedural modifications endorsed by ASTM. These modifications are explained by the fundamental behavior of non-newtonian fluids in capillaries.Current ASTM HTHS viscosity measurements use instruments in one of two categories: rotational or capillary. An initial discrepancy between the results from these two geometries motivated ASTM to re-examine the basics of HTHS viscometry, and resulted in modifications to the capillary procedures. These modifications were supported by limited experimental data suggesting the elimination of the previous discrepancy. This paper explains the physical cause of the discrepancy and the success of the procedural modification.