Properly estimating the protective effect of slender walls made of fine-grained concrete under dynamic loading is a major task in civil engineering. The aim of this contribution is to analytically describe the wave propagation in such a structural element reinforced with steel fibres. The analytical model may be an addendum to experimental studies and can be coupled to numerical methods. In a first step of modelling shear waves are dealt with. Within the mechanical model every reinforcement element is treated as a single inclusion surrounded by a so-called interphase embedded in a homogeneous matrix of fine-grained concrete. The differential equations resulting from this mechanical model are then solved analytically. In civil engineering praxis structural elements produced on-site regularly differ from the intended configuration. These deviances are exemplarily taken into account by modelling the thicknesses of the interphases surrounding the reinforcement elements as random variables. The consequences of this consideration to the wave propagation are presented and evaluated.