Abstract: An efficient algorithm to determine the intersection status between arbitrarily oriented ellipsoids and boxes (OBBs) is presented. By choosing a proper representation of the geometric objects and by utilizing an affine transformation of space, th problem is converted into a corresponding sphere-parallelepiped intersection test. thereby, the evaluation of more costly mathematical operations other than a constant number of simple arithmetic operations and comparisons can be avoided. Further efficiency is also gained by exploiting the regularity of the involved geometric shapes, as well as early rejection tests. Practical experiments show a four-times speed-up on average when these techniques are used.