or, "...in this school's 86th..."

It's not really necessary to say "this school" as it's obvious that only schools HAVE graduating classes, but saying "our" makes the register a bit informal, which might not go with what you want.

Alternatively, try "XX graduated with our 86th graduating class" -- but it's a little repetitious IMHO.

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Note added at 2003-06-26 05:39:27 (GMT)
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Using the number of the class (since the school\'s founding) is common in Chinese, but we tend to use the year of graduation in English -- which can admittedly cause problems if you\'re running some kind of training program which might graduate several classes per year.

在中国大陆，学校的毕业班通常按毕业年份排序的，但仍然沿用“届”字，实际上与一般的用法有距离。因此，“八六届”应该解释为1986年毕业的那一届。

据我所知，中国大陆的学校很少有按建校以来第多少届来为毕业班排序的。有少数不按年度毕业的情况，如几年一届，或一年几届，则以“期”名之，如黄埔三期。

学生在校期间，通常按入学的年份排序，因为谁也保不准都能毕业，名之为“级”，与毕业班的“届”区别。例如“八六级”就是1986年入学的那一级。

所以，我认为Kvasir 的第一个译法比较妥当。