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The present paper is focused on time-like circular surfaces and singularities in Minkowski 3-space. The timelike circular surface with a constant radius could be swept out by moving a Lorentzian circle with its center while following a non-lightlike curve called the spine curve. In the present study, we have parameterized timelike circular surfaces and examined their geometric properties, such as singularities and striction curves, corresponding with those of ruled surfaces. After that, a different kind of timelike circular surface was determined and named the timelike roller coaster surface. Meanwhile, we support the results of this work with some examples.