High purity, high cubicity aluminium foils were electrochemically etched in HCl-based etchants at constant anodic current density to produce etch tunnels. Tunnel widths were measured as a function of the etching depth, for temperatures in the range 60 to 95 degrees C and HCl concentrations in the range 0.1 to 9 N. The effect of sulfate and glycerol additions was examined. For HCl concentrations above 0.5 N, over most of the tunnel length, the widths w taper exponentially with depth x(1) i.e., w = w(0) exp(-x/2L), where w(0) is the tunnel width at the surface, and L is a characteristic length, here called attenuation length. For a defined set of experimental conditions, each tunnel has a unique value of to, but the same value of L. The tunnel taper increases with increasing temperature Tunnel velocity and attenuation length vary with temperature in an Arrhenius relationship, in such a way that their product is almost independent of temperature. The relationship between current density and tunnel taper is similar to a criterion reported for stable pit growth, suggesting a common mechanism. A quantitative model of tunnel growth, in which a salt film is assumed to be present at the tunnel tip, is developed. It predicts a relationship between the tunnel velocity, taper and saturation concentration similar to that observed.