In this paper we look at the Line Integral Convolution method for flow visualiz ation and ways in which this can be applied to the visualization of two dimensional, steady flow fields in the presenc e of uncertainty. To achieve this, we start by studying the method and reviewing the history of modifications oth er authors have made to it in order to improve its efficiency or capabilities, and using these as a base for the visu alization of uncertain flow fields. Finally, we apply our methodology to a case study from the field of oceanogr aphy.