The frictional interface at the moment of transition from static to dynamic state may undergo two types of disturbances: rupture-fronts and stress waves. Rupture-fronts are driven by the fracture of micro-contacts of the frictional interface, change the shape of the frictional interface, and propagate within the frictional interface under different speeds. By contrast, stress waves are driven by radiation from kinds of resources on the frictional interface, and have no effect on the shape of the frictional interface. Both rupture-fronts and stress waves imply important information of the dynamic behavior of frictional interfaces in nature. Here, stress wave structures associated with a frictional interface are studied for a finite-sized slider subjected to impact loading. First, SHPB experiments for frictional sliding of two glass sliders under shock wave loading are performed, and the fine wave structures near the frictional interface are directly measured with high-sensitivity piezoelectric sensors. The characteristics of stress waves related to the frictional interface are then simulated by finite element method for different frictional boundaries and constitutive model parameters to analyze the factors affecting stress wave propagation and profiles. Finally, the generation mechanism of the wave structures within the frictional interface is discussed based on the theory of the 1D stress wave. A new stress wave structure is first found experimentally and numerically. Unlike the traditional “rupture-fronts” phenomenon, this new wave, though generated from the overall dynamic response of the frictional interface, does not travel along the interface. Instead, it propagates perpendicularly to the interface as a plane longitudinal wave into the substrate. More interestingly, this new plane stress wave exhibits discretization enhancement in time but weaker in space. Within wave theory and simulations, it is found that the new wave does not stem from the fracture of micro-contacts on the frictional interface, but rather from the envelope of the spherical wave fronts radiated by the entire interface. This discovery reveals a new stress wave structure coming from frictional interfaces and its discretization characteristics, which is expected to provide a new stress wave structure criterion for earthquake prediction and non-destructive testing of engineering components.