This paper presents the investigation of the dynamic behaviour of concrete material under high strain rate tension using an interface approach in a mesoscale model framework. A rate-dependent cohesive constitutive description is introduced into the mesoscale framework to account for the effects of viscosity occurring in the dynamic fracture process. An algorithm is developed to insert cohesive elements throughout the mesoscale mesh grids in a concrete specimen, and to identify the cohesive element properties based on the original mesoscale structure. After parameter studies in terms of the cohesive element properties, the proposed model is validated against representative experimental data. The model is then employed to investigate the dynamic tensile behaviour of concrete under high strain rates. The underlying mechanisms of the dynamic tensile strength increase of concrete, including the influence of viscous effect from rate-dependent material description, the inertial effect from cracking and the material heterogeneity, are discussed and identified respectively. Results demonstrate that the viscous effect should be incorporated into the cohesive constitutive law to account for the Stefan effect at low and moderate strain rates and the micro-crack inertial effect only plays a significant role at a relatively high strain rate. Material heterogeneity does influence the strength enhancement under dynamic loading and the significance of this effect increases with the strain rate.