Abstarct: The behavior of viscoelastic materials has many applications in aerospace, petroleum, polymer, marine equipment, road construction and medicine industries. Viscoelastic behavior is a combination of elastic solid and viscous fluid properties. The relationship between stress and strain in viscoelastic behavior is time-dependent. The behavior of viscoelastic materials at a particular moment depends on the current loading conditions and, in addition, on the loading history. In this research, firstly, the formulation of the radial point interpolation(RPIM) elementless method for the analysis of viscoelastic problems using the integral equation in the time interval is presented. The behavior of the viscoelastic material is also considered linear, and the general Peroni series is used to model the viscoelastic behavior of the material. In each time step of the analysis of these problems, many domain integrals must be calculated. Gauss method is used in most of the elementless methods for the approximation of domain integrals. In this method, background meshing is needed, and in problems with complex geometries, it is necessary to spend a lot of computational cost to calculate the integrals with high accuracy. In the present study, domain integrals are calculated using the Cartesian transform method (CTM) with higher accuracy and speed than the Gauss method, which is a truly element-free method.