A novel approach to the analysis of the electrorheological effect is proposed, based on the expansion of dimensionless relative shear stress as function of electric field strength in the power series . The application of this approach to investigation of the electrorheological effect in suspensions of isotropic and needle-like CeO2 nanoparticles in polydimethylsiloxane has revealed that the polynomial coefficients can be judged as a measure of the efficiency of transformation of electrical energy into mechanical energy. The values of alpha and beta coefficients depend on the shape and concentration of filler particles, as well as on the shear rate. The value and the sign of these coefficients determine both the magnitude of the electrorheological effect and the type of dependence of the shear stress (linear or power law) on the strength of the electric field. It has been shown that the values of alpha and beta coefficients for the electrorheological fluids with needle-like particles are greater than for fluids with isotropic particles (at the same concentration of suspensions), which is associated with the different polarization of particles in the applied electric field.