This work presents a study of the influence of dielectric permittivity on the interaction between a positive pulsed He plasma jet and a 0.5 mm-thick dielectric target, using a validated two-dimensional numerical model. Six different targets are studied: five targets at floating potential with relative permittivities ϵr= 1, 4, 20, 56 and 80; and one grounded target of permittivity ϵr=56. The temporal evolution of the charging of the target and of the electric field inside the target are described, during the pulse of applied voltage and after its fall. It is found that the order of magnitude of the electric field inside the dielectric targets is the same for all floating targets with ϵr≥4. For all these targets, during the pulse of applied voltage, the electric field perpendicular to the target and averaged through the target thickness, at the point of discharge impact, is between 1 and 5 kV cm−1. For the two remaining targets (ϵr=1 and grounded target with ϵr=56), the field is significantly higher than for all the other floating targets.