Results of a tight binding calculation of the transmission probabilities of electrons through GaAs/strained GaAsP/GaAs(100) heterostructures are presented. The GaAsP layer thicknesses considered are sufficiently thin that the GaAs/GaAsP lattice mismatch is accommodated by layer strain rather than dislocation generation. For layers with small GaP content, incident electrons in Bloch states near Γ can transport through the alloy in Bloch states that are also near Γ. Transmission probabilities are large and exhibit resonant (total) transmission at GaAsP layer thicknesses determined by the wavevector k of the accessible GaAsP Bloch states. For layers with large GaP content, incident electrons must either ’’tunnel’’ through the GaAsP evanescent states associated with the Γ minimum or undergo phononless intervalley transfer at the interface to the accessible Bloch states near X in GaAsP. For extremely thin GaAsP layer (less than a few lattice constants), the tunneling type process dominates. The phononless intervalley transfer process is found to occur with very small probability except for carrier energies and layer thicknesses corresponding to resonant transmission.