Non-uniformity and anisotropy of the conductivity of a liquid flowing through an electromagnetic flowmeter affects its sensitivity. This effect is analysed for a circular meter with small electrodes and rectilinear flow with an axisymmetric velocity profile. The magnetic field is assumed invariant in the flow direction. The conductivity tensor is assumed to have principal axes in the radial and azimuthal directions with the principal conductivities σ_r, σ_θ depending only on the radius. The sensitivity is found analytically for an arbitrary plane magnetic field in the case σ_rσ_θ=constant. When the field is uniform the condition on σ_r and σ_θ necessary to make the sensitivity independent of the shape of the velocity profile is found. The sensitivity change is deduced for small perturbations from this conductivity distribution, for an arbitrary axisymmetric velocity profile. The effect of blood vessel walls having large conductivity variations of a simple type is also found. The results agree well with the numerical calculations of Baker in 1970 and satisfactorily with deductions made from the experimental results of Phibbs in 1968 and Dennis and Wyatt in 1969.