Abstract：The localization of damage variable (rate) is investigated. Based on non-local theory，the damage variable is non-local variable and is dependent on local damage variable and its second spatial gradient. After onset of damage localization，the constitutive relation is considered linear strain softening. The boundary condition between elastic and damage zones where the local damage is zero is used and the assumption that the width of damage zone is determined according to maximum local damage variable is adopted. The analytical solutions of local damage variable，local damage variable rate and width of localized damage zone at strain softening period are obtained. Besides，the presented definition on relation among tensile stress，tensile strain and non-local damage variable is different with traditional expression in that the coefficient of non-local damage variable is 2，not 1，in the presented definition. The advantage of the present definition is that when specimen is completely separated into two pieces，the maximum local damage variable can reach 1，which agrees with general knowledge. The average value of local damage variable in the rang of damage localization zone is the non-local damage variable. In addition，the maximum local damage variable is two times of the average damage variable.
