Abstract: Marine riser is a critical component of a floating vessel drilling system. This paperpresents a time-domain dynamic analysis of marine riser by the finite element method. By taking a higher order displacement model, a fairly small number of elements can result in a satisfactory solution. And thus the computation time can be greatly reduced. In the ease of risers analyzed in the paper, convergent results are obtained by using only three or five elements. The responses of risers to regular or irregular waves are all covered in the paper. Irregular waves are treated as summation of a series of regular waves.