Einstein computed the apparent viscosity of a dilute suspension of neutrally buoyant spheres in an incompressible Newtonian fluid. The objective here is to determine the apparent stress‐deformation behavior of a dilute suspension of neutrally buoyant spheres in an incompressible power model fluid. With the assumption thatη=mγn−1describes the apparent viscosity of the continuous phase, our analysis predictsη(sus)=(1+c0x)mγn−1as the apparent viscosity of the dilute suspension of spheres. Here γ is the shear rate,mandnare the power model parameters for the continuous phase, andxis the volume fraction of spheres in the suspension. The coefficientc0is defined by the rate of energy dissipation within the neighborhood of a typical sphere in the suspension. In order to evaluate this rate of energy dissipation, the velocity distribution is required. In the limitn=1,corresponding to an incompressible Newtonian fluid, Einstein was able to solve the equations of motion and foundc0=2.5.Forn≠1,the equations of motion are nonlinear and have not yet been integrated. Instead, we have used previously available principles to calculate upper and lower bounds for the rate of energy dissipation within the neighborhood for a single sphere. This results in upper and lower bounds forc0as a function ofn. The average of these bounds forc0is compared with available experimental data.