Rolling resistance is the common name used when a moment that opposes the rolling motion of a particle is introduced into the modeling. This moment is usually incorporated as a practical way to represent the effect of non-sphericity on rolling spheres or the effect of surface irregularities on other type of particles. Two rolling resistance models are available in Rocky, which are described in the following sections.
In this model, a constant moment is applied to the particle in order to represent rolling resistance. The mathematical expression for this moment is:
 | (2–32) |
where:
is the rolling resistance coefficient, defined in Rocky as a particle
property listed simply as Rolling Resistance. Ai et al. [15] define this dimensionless parameter as the tangent of the maximum
angle of a slope on which the rolling resistance moment counterbalances the moment
produced by gravity in the particle. 
is the contact normal force. 
is the particle angular velocity vector. The direction of the rolling
resistance moment vector will coincide with the direction of this angular velocity. 
is the particle rolling radius, where 
is the vector joining the centroid of the particle and the contact
point.
The rolling resistance model type A only should be used in situations when a high angle of repose is needed without using adhesive force models.
This is an elastic-plastic model that is the recommended one for most simulations that need to include the effects of rolling resistance. Models of this type usually include a viscous damping term in order to suppress oscillations. However, as Wensrich & Katterfeld [16] argue, the proper choice of the rolling stiffness value provides a good behavior of the rolling resistance without the need of additional damping. This is the approach followed in Rocky, where the rolling stiffness is defined as:
 | (2–33) |
where 
is the tangential stiffness, defined in Equation 2–19,
whereas 
is the rolling radius, given by:
 | (2–34) |
in which 
and 
are the rolling radii of the contacting particles, while 
is the rolling radius of a particle in contact with the boundary. The
rolling radius vector is defined as the vector joining the centroid of the particle and the
contact point at a given time.
If the rolling resistance were purely elastic, the rolling resistance moment would be updated incrementally in the following way:
 | (2–35) |
where:
is the rolling resistance moment vector at the previous time.
is the rolling stiffness defined in Equation 2–33. 
is the relative angular velocity vector, which is defined as the
difference between the angular velocities of two contacting particles or the angular
velocity of a particle on a boundary, as the case may be. 
is the simulation timestep.
The updated rolling resistance moment defined in Equation 2–35 is not used directly in the motion equation for the particles. In the rolling resistance model type C, the magnitude of the rolling resistance moment is limited by the value which is achieved at a full mobilization rolling angle. The limiting value is:
 | (2–36) |
where:
is the rolling resistance coefficient, defined in Rocky as a particle
property listed simply as Rolling Resistance. As stated previously,
this dimensionless parameter is defined as the tangent of the maximum angle of a slope
on which the rolling resistance moment counterbalances the moment produced by gravity in
the particle. 
is the rolling radius defined in Equation 2–34
is the contact normal force.
The final expression for the rolling resistance moment in model type C is:
 | (2–37) |