The methods of plastic limit analysis are used to determine the indentation pressures of a flat rigid punch on a columnar ice sheet. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. Representative strength parameters of columnar sea ice are used to define anisotropic yield criteria for the ice sheet. The anisotropic yield criteria reflect the variations in mechanical properties caused by the horizontal orientation of the c-axis of sea ice in the columnar zone. Numerical results are obtained by applying the lower-bound theorem of plastic limit analysis. A three-dimensional stress field is optimized for a given ice condition for various indentor sizes. The effects of varying the aspect ratio (defined as the ratio of indentor width to ice thickness) are then addressed. A comparison of results for intermediate aspect ratios to results for extremely high (plane stress) and extremely low (plane strain) aspect ratios is presented. It is found that the transition from plane stress to plane strain is governed by the tensile strength of the ice medium.