  Up to now, all charge radius measurements of the proton and deuteron assumed
uniform spheroidal charge distribution. We investigate the nuclear deformation
effects on these charge radius measurements by assuming a uniform prolate
charge distribution for the proton and deuteron. We solve the energy levels of
the corresponding muonic and electric atoms with such deformed nucleus and
present how the purely quadruple deformation of proton and deuteron affects
their Lamb shifts. The numerical results suggest that the deformation of proton
and deuteron leads to that the charge radius extracted from the electronic
measurement should be smaller than the corresponding one in the muonic
measurement which assumed uniform spheroidal charge distribution. If the
central values of newest measurements for the proton are adopted, the proton
would have a prolate structure with the 0.91 $\mathrm{fm}$ long axis and 0.73
$\mathrm{fm}$ short axis. Further improved precise charge radius measurements
of the proton and deuteron will help us to pin down their shape deformation.
