The Non-Smooth Contact Dynamics (NSCD) approach is widely consolidated in the dynamics of rigid blocks structures. Its application to masonry has been investigated in some recent relevant papers, see for instance [1]. The approach is effective to study the dynamic response of structures where the arrangement of the elementary units has a predominant role. Within the context of masonry, the elementary units are the individual bricks and are characterized by a parallelepiped shape. However, it is not unusual to find structures composed of units with curved shapes (for instance, it is the case of Gothic arches). A recent paper from the author discussed the influence of curved geometry in the load-bearing capacity of such structures [2]. Therefore, here we present a NSCD approach enriched with a geometrical modelling strategy based on NURBS solids (where NURBS stands for Non-Uniform Rational B-Spline), capable of takin into account rigid blocks of curved shapes. A NURBS solid, i.e. a closed volume defined by boundary surfaces, is used to represent the geometry of each curved block: this allows determining geometrical and mass properties through a suited surface integral. The equations of motion are expressed for each block through the impulse theorem format: at each time step, the applied forces during the current range of time generate variations in the overall momentum, which are quantified as increment in the blocks velocities. Also, normal and tangential impulses act at the contact points between adjacent blocks, to which a frictional contact law is assigned. The contact points are determined using the well-known GJK algorithm combined with a point inversion algorithm conceived for NURBS surfaces. For each time step, the overall problem is written as a second order conic programming problem and its solution provides the blocks velocities at the current time.