Quadrature element formulations for tapered partially steel-concrete composite beams were established based on the Newmark model and the plane stress model respectively. Deformation of tapered partially composite beams under distributed loading and free vibrational problems with two representative boundary conditions were examined. It is shown that for slender and slightly tapered composite beams common in engineering the proposed 1D quadrature element model is effective enough for flexural and fundamental frequency analysis. Moreover, the 2D quadrature element model is capable of providing better results when needed.