Human tissue consists of cells suspended in an aqueous medium. As a consequence, the electrical conductivity of a tissue is inhomogeneous on a microscopic scale. On a macroscopic scale the conductivity of a tissue can be considered to be homogeneous, and this conductivity is called the effective conductivity. In this paper a theory is presented to estimate this effective conductivity. On a cellular scale, the tissue will be modelled as a suspension of ellipsoidal cells. On a somewhat larger scale, it will be modelled as a layered structure, as most tissues can be described by layers that differ in conductivity. For both scales, upper and lower bounds for the effective conductivity will be estimated. The more information on the shape, orientation, conductivities, and distribution of the cells or layers is available, the more strict these limits are. The effective conductivity will be evaluated for several tissues, such as the cerebral cortex, the liver, and blood.