Pipeline operators commonly use means of temporary crossing such as timber-mat, airbridge, and slab to reduce surface loading induced stresses in a buried pipeline at locations where a heavy vehicle crosses the buried pipeline. When a temporary crossing has a continuous contact with soil, (e.g. timber mat, flexible slab) load distribution over the ground surface is not immediately known. Load distribution under a timber-mat or flexible slab is a function of the slab to soil stiffness ratio. The load distribution tends to become more uniform with increasing timber-mat or slab stiffness. In this work an analytical model using beam-on-elastic-foundation has been developed and Laplace transform has been utilized to find the solution and apply free-end boundary conditions. The analytical solution can be used for any arbitrary load distribution over a beam-on-elastic foundation. In this work the solution for a point load and a partially distributed uniform load were employed as these scenarios can accurately represent conventional vehicle foot-prints, while being computationally efficient. The analytical solutions are compared to finite element analysis to validate the model. This model can be used in conjunction with the Canadian Energy Pipeline Association (CEPA) surface loading calculator (or similar tools) to analyze pipeline encroachment problems when means of temporary crossing is installed. This model can help the operators determine dimensions and bending stiffness of timber-mat or flexible slab to assure a desirable load distribution will be achieved. The model can also be used for structural analysis of a timber-mat or flexible slab under vehicular load.