Magnetic resonance and ultrasound elastography techniques are now important tools for staging high-grade fibrosis in patients with chronic liver disease. However, uncertainty remains about the effects of simple accumulation of fat (steatosis) and inflammation (steatohepatitis) on the parameters that can be measured using different elastographic techniques. To address this, we examine the rheological models that are capable of capturing the dominant viscoelastic behaviors associated with fat and inflammation in the liver, and quantify the resulting changes in shear wave speed and viscoelastic parameters. Theoretical results are shown to match measurements in phantoms and animal studies reported in the literature. These results are useful for better design of elastographic studies of fatty liver disease and steatohepatitis, potentially leading to improved diagnosis of these conditions.