We have developed a method for measuring fiber kinematics in two-dimensional soft collagenous tissues. The technique combines small-angle light scattering (SALS) and biaxial stretch controlled by simultaneous optical strain measurement. Preliminary findings on porcine aortic valve leaflets and bovine pericardium indicate that fiber kinematics are highly tissue specific and are generally non-affine. The mobility of the fibers within each tissue seems to be specialized to perform a distinct physiological function. Quantitative knowledge of a tissue's angular fiber distribution and its transformation during biaxial stretch is critical for microstructural modeling of planar tissues. Our results underscore the importance of measuring fiber kinematics for each specific tissue type that is to be modeled.