By stretching the rod waveguide with different velocities in opposite directions,the tapered waveguide can be fabricated.In condition of taking no account of volume expansion caused by heating and under the assumptions of volume conservation,the rod waveguide can be stretched freely in the heated region without being stretched outside of the heated region. A model,which shows the relation of the transition shape and the two factors,that is the ratio of two velocity and the heated region length,is presented for the shape of the taper transition through mathematic deduction.Based on this model,a desired tapered waveguide can be fabricated.The tapered waveguide are widely used for fabricating tapered fiber couplers and sensors.In addition,the conclusion can be used for fabricating fused fiber coupler. By stretching the rod waveguide with different velocities in opposite directions, the tapered waveguide can be fabricated.In condition of taking no account of volume expansion caused by heating and under the assumptions of volume conservation, the rod waveguide can be stretched freely in the heated region without being stretched outside of the heated region. A model, which shows the relation of the transition shape and the two factors, that is the ratio of two velocity and the heated region length, is presented for the shape of the taper transition through mathematic deduction .Based on this model, a desired tapered waveguide can be fabricated. The tapered waveguide are widely used for fabricating tapered fiber couplers and sensors. In addition, the conclusion can be used for fabricating a fused fiber coupler.