The aim of this paper is to suggest a procedure to analyse the supporting brace stiffness influence on the damping optimization of a linear-elastic shear-type model. This analysis appropriately extends the Takewaki's technique based on the minimization of an objective function, which represents the sum of mean-square inter-storey drifts to stationary random excitation. The new procedure is a two-phase optimization technique in which an optimal value of the supporting brace stiffness is also involved. In order to demonstrate the applicability of the proposed procedure, the results of the numerical analysis for an 8-dof shear-type model subjected to a base excitation are presented. Moreover, response in the time domain is worked out for the analysed model. The procedure presented in this paper is readily available for practical applications. Copyright (C) 2008 John Wiley & Sons, Ltd.