•A dynamic model successfully validated for modelling residential buildings equipped with EAHE is developed.•The building indoor conditions in summer can be significantly enhanced by using EAHE and insulation.•The insulated light buildings are more effective than the insulated heavy buildings in hot and arid climate.•Effect of building materials, including insulation materials, combined with that of EAHE is also investigated.•Due to its influence, the building geometrical aspect is a parameter which should be carefully chosen. This paper aims to investigate the impact of the thermal insulation on the cooling effectiveness of the Earth-to-Air Heat Exchanger systems under hot and arid climate. For that, the dynamic behaviour of two identical buildings submitted to the same exterior solicitations and equipped with an EAHE is presented in detail. To achieve the objective of this study, two transient models are developed; one for modelling the EAHE and the other for describing the thermal behaviour of buildings. The set of differential equations corresponding to different components of the system is solved using the technique of Complex Finite Fourier Transform. The findings indicate that when the insulated building is equipped with an EAHE, the effect of the thermal insulation will be combined with that of EAHE and the resulting effect will be more important, so that the reduction in the indoor air maximal temperature can be greater than 11°C and the reduction rate in the amplitude of the indoor air temperature increases until 91%. In addition, it is found that the thermal performances of the building outer walls represented usually by the decrement factor and the time-lag can be more improved using insulation layers within these components. On the other hand, the investigation conducted on the effect of the building materials showed that in Saharan climate, the light buildings such as those constructed with autoclaved aerated concrete blocks are more performing compared to the heavy buildings in which the outer walls must be judiciously insulated with a material of high thermal resistance. However, it is shown that the insulation with air cavities is an effective and economic solution for the light buildings in hot and arid regions.