By using the analytical Flamant and Melan solutions

the integral formulae derived from Mindlin’s equations

solutions in semi-infinite plane are derived to calculate displacements and compare with computed results from the finite element method. It is found that the calculated displacements are indeterminate in the line loading direction

where no absolute displacements but only relative displacements can be obtained. However

the calculated relative displacements increase with an increasing in the distance away from the reference point of displacement constraint; and they also increase with an increasing length of line load distribution normal to the half-plane

leading to non-convergence. This means the derived displacement solutions of pure half-plane problems are multivalued. Thus

it is necessary to analyze geotechnical problems using the half-space assumption.