${\mathrm{P}\mathrm{b}\mathrm{T}\mathrm{e}/\mathrm{P}\mathrm{b}}_{0.88}$${\mathrm{Sn}}_{0.12}$Te Te superlattices were prepared with individual thicknesses of about 50 nm and periodicities of 100-250 nm on ${\mathrm{BaF}}_{2}$ substrates. The lattice constant mismatch of $\frac{\ensuremath{\Delta}a}{a}=2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ introduces a misfit strain in the constituent layers and there is an additional tensile strain caused by the substrate. These strains were determined by x-ray diffractometry. The electrical properties of this many-valley type-I superlattice were investigated by conductivity, Hall effect, and weak-field magnetoresistance (WFMR) experiments. For electrons or holes confined in the Pb-Sn-Te layers, the angular dependence of the WFMR data is consistent with quasi-two-dimensional transport. The band structure of these many-valley PbTe/Pb-Sn-Te superlattices is calculated by matching propagating or evanescent envelope functions at the boundaries of consecutive layers and considering the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ Hamiltonian for cubic IV-VI compounds at the $L$ point of the Brillouin zone. The evolution of the PbTb/Pb-Sn-Te band structure with increasing superlattice periodicity is calculated and energy-momentum dispersions are given for the samples of interest. The observed quasi-two-dimensional transport is explained by these $E(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ relations, yielding, for appropriate superlattice periodicities, cylinders as surfaces of constant energy.