Point bar reservoir geology is frequently encountered in oil and gas developments worldwide. Furthermore, point bar geology is encountered in many sites being considered for large scale CO2 injection for sequestration. A comprehensive modeling method that adequately preserves point bar internal architecture and its associated heterogeneities is still not available. Traditional geostatistical methods cannot adequately capture the curvilinear architecture of point bars. Even geostatistical simulation techniques that can be constrained to multiple point statistics cannot capture the architecture of the point bars because they use regular grids to represent the heterogeneity. If heterogeneities like the thinly distributed shale drapes within the point bar are represented using an extremely fine mesh, the computational cost for performing flow modeling escalates steeply. This paper proposes a modeling method that preserves the point bar internal architecture and heterogeneities, without these limitations. The modeling method incorporates a gridding scheme that adequately captures the point bar architecture and heterogeneities, without huge computational costs.