Steady state natural convection heat transfer in a longitudinally short rectangular fin array on a horizontal base is numerically investigated. The problem is three dimensional laminar natural convection heat transfer with open boundaries. A finite difference code based on vorticity-vector potential approach is developed to solve the governing equations. The steady behaviour of the flow and temperature distributions is obtained from the solution of transient form of the governing equations. Results are compared with the available experimental results in the literature. A good agreement is seen between the numerical and reported experimental results. Flow configurations occurring in the channel of the fin arrays with different geometrical parameters, (fin length, fin height and fin spacing) are analysed. Based on the obtained results, two types of flow patterns are observed. The mechanisms of the flows are discussed and flow patterns are plotted to support the discussion. The study is limited to Rayleigh number based on fin spacing, ranging from 120 to 39000. The fin length and fin height are varied from 2 to 20 and 0.25 to 7-fin spacing, respectively.