We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven by a uniform steady state shear strain applied at a fixed finite rate. Energy dissipation occurs via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension and resulting in a Newtonian rheology. We study the resulting pressure p and deviatoric shear stress σ of the interacting spherocylinders as a function of packing fraction φ, strain rateγ, and a parameter α that measures the asphericity of the particles; α is varied to consider the range from nearly circular disks to elongated rods. We consider the direction of anisotropy of the stress tensor, the macroscopic friction µ = σ/p, and the divergence of the transport coefficient ηp = p/γ as φ is increased to the jamming transition φJ . From a phenomenological analysis of Herschel-Bulkley rheology above jamming, we estimate φJ as a function of asphericity α and show that the variation of φJ with α is the main cause for differences in rheology as α is varied; when plotted as φ/φJ rheological curves for different α qualitatively agree. However a detailed scaling analysis of the divergence of ηp for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We also compute the number of contacts per particle Z in the system and show that the value at jamming ZJ is a non-monotonic function of α that is always smaller than the isostatic value. We measure the probability distribution of contacts per unit surface length P(ϑ) at polar angle ϑ with respect to the spherocylinder spine, and find that as α → 0 this distribution seems to diverge at ϑ = π/2, giving a finite limiting probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally we consider the variation of the average contact force as a function of location on the particle surface.