This paper proposes two regularized models of the μ (I)-rheology and shows their application to the numerical simulation of 3D dense granular flows. The proposed regularizations are inspired by the Papanastasiou and Bercovier–Engleman methods, typically used to approximate the Bingham law. The key idea is to keep limited the value of the apparent viscosity for low shear rates without introducing a fixed cutoff. The proposed techniques are introduced into the Particle Finite Element Method (PFEM) framework to deal with the large deformations expected in free-surface granular flows. After showing the numerical drawbacks associated to the standard μ (I)-rheology, the two regularization strategies are derived and discussed. The regularized μ (I)-rheology is then applied to the simulation of the collapse of 2D and 3D granular columns. The numerical results show that the regularization techniques improve substantially the conditioning of the linear system without affecting the solution accuracy. A good agreement with the experimental tests and other numerical methods is obtained in all the analyzed problems.