The synthesis and crystallography, magnetic susceptibility χ, magnetization M , specific heat Cp, in-plane electrical resistivity ρ and in-plane magnetic penetration depth measurements are reported for single crystals of APd2As2 (A = Ca, Sr, Ba) versus temperature T and magnetic field H. The crystals were grown using PdAs self-flux. CaPd2As2 and SrPd2As2 crystallize in a collapsed body-centered tetragonal ThCr2Si2-type structure (I4/mmm), whereas BaPd2As2 crystallizes in the primitive tetragonal CeMg2Si2-type structure (P 4/mmm), in agreement with literature data. The ρ(T ) data exhibit metallic behavior for all three compounds. Bulk superconductivity is reported for CaPd2As2 and SrPd2As2 below Tc = 1.27 and 0.92 K, respectively, whereas only a trace of superconductivity is found in BaPd2As2. No other phase transitions were observed. The χ(T ) and M (H) data reveal anisotropic diamagnetism in the normal state, with χc > χ ab for CaPd2As2 and BaPd2As2, and χc < χ ab for SrPd2As2. The normal and superconducting state data indicate that CaPd2As2 and SrPd2As2 are conventional type-II nodeless s-wave electron-phonon superconductors. The electronic superconducting-state heat capacity data for CaPd2As2, which has an extremely sharp heat capacity jump at Tc, are analyzed using our recent elaboration of the α-model of the BCS theory of superconductivity, which indicates that the s-wave gap in this compound is anisotropic in momentum space.