As the key structure of a practical construction technique, the low-cement extruded curb has been widely used in recent concrete-faced rockfill dams (CFRDs). The extruded curb exhibits significant interactions with the neighboring gravels and with the face slab. These interactions were investigated using element tests, and a new model was proposed. This model is composed of three parts: (i) the equivalent slab that is described using an ideal elastoplasticity model, (ii) the equivalent interface between the curb and the gravel cushion layer that is described using an elastoplasticity damage model, and (iii) the interface between the curb and the face slab that is described using a modified ideal elastoplasticity model. This model was verified via a two-dimensional numerical simulation of an ideal CFRD to capture the main behavior of the extruded curb with interactions between the extruded curb and the neighboring soil – face slab, employing a significantly smaller number of elements and a shorter calculation than direct simulation. The model was used to perform a three-dimensional stress–displacement analysis of the Bakun CFRD (205 m in height), and the results showed that the extruded curb causes a change in the stress of the face slab.