In the open ocean, many animals are highly transparent, some achieving near invisibility. However, little is known about how this transparency is attained. The effects of cellular ultrastructure on tissue transparency were mathematically modeled. Given a specific constant volume or surface area of a higher refractive index material (e.g. protein, lipid, etc.), within a lower refractive index cytoplasm or other matrix, the model calculates the total amount of light scattered as a function of how the volume or surface area is subdivided. Given a constant volume, the scattering peaks strongly when the volume is divided into spheres of critical radii. The critical radii depend upon the refractive index of the material relative to its surroundings. Similarly, given a constant surface area, the scattering increases rapidly with sphere size until critical radii (approximating the critical radii for constant volume) are reached, after which the scattering is relatively constant. Under both constraints, refractive index is critical when the particles are small, but becomes progressively less important as particle size increases. When only forward scattering is considered, the results are essentially similar to those found for total scattering. When scattering at only larger angles is considered, the critical radii are independent of refractive index, and the scattered radiance depends critically on refractive index at all particle sizes. The effects of particle shape on scattering depend on the geometric constraint and particle size. Under constant volume constraints, small particles of any shape scatter light equally, but large spheres scatter less light than other larger shapes. Under constant surface area constraints, small spheres scatter more light than any small shape, but large particles of any shape scatter equally. The effects of crowding and the refractive index of the surrounding medium on these predictions are discussed. Copyright 1999 Academic Press.