The resilient fastener slab track (RFS track) has found extensive application in urban railways, effectively mitigating vibration and noise resulting from train operations. However, the structure elasticity of the RFS track is higher than the normal slab track (NS track), which can affect train running stability and cause abnormal vibration phenomenon. This paper explores the track structure elasticity on vehicle-track interaction and train running stability through experimental tests and numerical simulations. The vibrational properties of the RFS track and the NS track are obtained through field tests. A 3D metro vehicle-track coupled dynamics model is developed and utilized to simulate the dynamic performance of metro vehicles moving on different track structures. The impact of track structure parameters upon the vehicle-track interaction and train running stability are discussed. The findings indicate that the track structure elasticity can reduce train hunting stability and cause abnormal vibration phenomena in metro vehicles under certain conditions. The reasonable matching of the fastener lateral and vertical stiffness can not only accomplish vibration attenuation but also minimize the impact on train running stability. In addition, the rail surface wear and track gauge variation also exert influence on the running stability and dynamic performances of metro vehicles.