In this study, effects of wall's insulation thickness and position on time lag and decrement factor have been investigated numerically. For this purpose, one-dimensional transient heat conduction equation was solved using Crank-Nicolson scheme under convection boundary conditions. To the outer surface of the wall, periodic boundary conditions were applied. The total wall thickness (insulation+thermal mass = 20 cm) was kept constant in a such a way that when the insulation thickness was increased, the thermal mass thickness was decreased in the same amount. The insulation was placed in four different locations of the wall. These locations were the inner surface, the outer surface, the center plane and half of the insulation in the inner surface and half of the insulation in the outer surface of the thermal mass. For all these wall configurations, the computations were repeated and effects of wall's insulation thickness and position on time lag and decrement factor have been investigated. It was found that insulation thickness and position have a very profound effect on the time lag and decrement factor. Computations were repeated for three different insulation materials namely polyurethane foam, cork board and rubber and for two different thermal masses namely brick and wood and the results were discussed.