The current work is concerned about a two dimensional multi phase lag modelof generalised thermoelasticity in an isotropic half space medium. A vector-matrixdifferential equation is obtained from the governing equations using normal modeanalysis. The eigenvalue approach is applied to get the solutions. Numerical computationsfor different components of displacement, stress, strain and temperatureare calculated and represented graphically to show the accuracy in context ofmechanical and thermal loads that applied on the boundary.