As the casing undergoes bending deformation along the well trajectory, the contact position and state between the casing and wellbore exhibit dynamic variations during casing running operations in extended-reach wells. Assessing random contact between the casing and wellbore becomes critical for studying the mechanical properties of running casings. Hence, we utilized the Universal Mechanical Tester (UMT) pin-on-disk friction system to assess the kinetic and static friction coefficients of casing with surface casing and formation rock in mud environments, and employed the stochastic contact approach to develop a 3D dynamic finite element model incorporating the actual well trajectory. We conducted an analysis of the mechanical characteristics of running casings and discussed how factors such as wall thickness, friction coefficients, running speeds, and wellbore fluid density affect the mechanical distribution of casing. Numerical results indicate that the substantial frictional contact between the casing and the wellbore wall appears in the positive inclined and horizontal sections, and the casing initiates buckling behavior at a running depth of 3000 m. With the increase in running depth, the casings buckling behavior gradually transitions from sinusoidal to helical, causing a sharp increase in additional resistance against casing running. Finally, the casing cannot continue running beyond 4022 m. In comparison to the effect of wellbore roughness, the wall thickness of the casing and the fluid density primarily influence the horizontal well section. Furthermore, higher running speeds exacerbate buckling behavior by delaying the efficient release of the casings accumulated elastic energy.