<p>This paper is concerned with modeling inertia effects in materials. We propose elasticity-inertia models incorporating a novel element called inerter, which exhibits the property of equivalent inertia. Different from the existing works that capture inertia effects by strain gradients, the proposed models directly model general inertia effects by inerters. The stress-strain relationships of the proposed models are represented by spring-inerter networks, which resemble viscoelastic models represented by spring-dashpot networks. It shows that in the constitutive equations and dynamic equations of the proposed models, strain acceleration terms or micro-inertia terms can be easily and directly obtained without adding terms or using operator transformations. The dispersion and vibration properties of the proposed models are derived analytically. The discretization methods are presented as well for obtaining numerical solutions of the proposed models. The proposed elasticity-inertia models provide a very natural way in capturing inertia effects, offering an alternative perspective for modeling inertia effects in materials.</p>