We investigate how the frequency-dependent wave propagation coefficient and complex modulus for a linearly viscoelastic material can be estimated From wave propagation experiments. The strains at different sections of a bar specimen are measured as functions of time. The time series are transformed into the frequency domain. where a non-parametric identification is made. A thorough analysis of the quality of the cion-parametric estimate is made, in which approximate expressions for the covariance matrices of the wave propagation coefficient and the complex modulus are derived. The validity of these expressions are confirmed by numerical studies and real experiments,