This work deals with the onstruction of a transponation plan for optimaltransportation methodology in Egypt. This plan takes place between the refineries andthe relevant bulk plants since the transportation cost is minimal.Three products are considered in the model: gasoline, kerosene. and fuel oil,which are produced from four refineries in Alexandria, Suez, Tanta, and Cairo.They are distributed to the various sectors in Egypt. Three transportation methods areused in this work: pipelines.” trucks. and railways. The model established is solvedfor the year 1985-1986 for the products in question. The optimal quantities to betransported by trucks, pipelines, and railways are established.The model is also solved for the years 1987 to 1991, and the results are alsoanalysed.A fictitious pipeline is supposed for the model between Alexandria andDamietta, passing through Kafre El-Sheikh and Mansura. This choice cas been mademodel is an inequality-constrained model, which concerns with thefrictionless thermoelastic contact problem. The mathematicalprogramming method is used to handle that model. Throughout thecontact interface both thermal and mechanical boundary conditions areinforced by using the convex programming procedure. Such procedure isapplied incrementally on the time domain of the problem.Several problems, with different geometries, boundary and loadingconditions are analyzed and examined by using the developed model. Thetemperature distribution and the contact status, including contact area andcontact pressure are predicted. Also, the effect of different distortivitiesupon the contact status is detected.The obtained results demonstrate clearly the efficient applicabilityof the developed model to handle the transient thermoelastic frictionlesscontact problems.