  We have studied the superconducting gap structure of LaPt$_2$Si$_2$ by
measuring the temperature dependence of the London penetration depth shift
$\Delta\lambda(T)$ and point contact spectroscopy of single crystals.
$\Delta\lambda(T)$ shows an exponential temperature dependence at low
temperatures, and the derived normalized superfluid density $\rho_{s}(T)$ can
be well described by a single-gap s-wave model. The point-contact conductance
spectra can also be well fitted by an s-wave Blonder-Tinkham-Klapwijk model,
where the gap value shows a typical BCS temperature and magnetic field
dependence consistent with type-II superconductivity. These results suggest
fully gapped superconductivity in LaPt$_2$Si$_2$, with moderately strong
electron-phonon coupling.
