Generally, Plan I is used by some people who are funded by government projects whose sponsors require them to write a thesis as a component/stipulation of their support. It is not a common plan. The primary differences between Plan I and Plan II are, Plan I requires 20 units and a thesis, while Plan II requires 24 units and an oral presentation and report.
For more information, please see http://me.berkeley.edu/graduate-student-handbook/52-master-science-degree-requirements-plan-i. A printable version of the curriculum can be found here.
Please note that the Department of Mechanical Engineering will not offer a standard Master of Science terminal degree option for the Fall 2019 application cycle. Students who are interested in a terminal master’s program may wish to consider our Master of Engineering Program.