Development of tolerance analysis methods that are consistent with the ASME and ISO GD&T (geometric dimensioning and tolerancing) standards is a challenging task. Such methods are the basis for creating computer-aided tools for 3D tolerance analysis and assemblability analysis. These tools, along with the others, make it possible to realize virtual manufacturing in order to shorten lead-time and reduce cost in the product development process. Current simulation tools for 3D tolerance analysis and assemblability analysis are far from satisfactory because the underlying variation algorithms are not fully consistent with the GD&T standards. Better algorithms are still to be developed. Towards that goal, this paper proposes an improved simulation-based approach to tolerance and assemblability analyses for assemblies with pin/hole floating mating conditions in mechanical products. A floating pin/hole mating condition is the one where the mating pin should be able to "float" within the mating hole, and thus press-fit is not necessary for the parts to assemble properly. When multiple pin/hole mating pairs are involved in a product, the feasibility of assembly needs to be analyzed. This paper will introduce a more complete method of analyzing assemblability for such assemblies. In most cases, a 3D (3-dimensional) problem can be simplified to 1D (1-dimensional) or 2D (2-dimensional) problem, with the loss of some accuracy. To make a comparison and find out how accurately 1D and 2D analyses can approximate 3D analysis, this paper will provide the variation algorithms for 1D, 2D and 3D simulations. The algorithms developed account not only for bonus/shift tolerances1 but also for feasibility of assembling. These algorithms are extendable to consider other different GD&T specifications. The assemblability criteria proposed is generally applicable to any assemblies with pin/hole floating mating conditions. Case studies are provided to demonstrate the algorithms developed. The comparison study shows quantitatively the difference in the results from 1D, 2D and 3D simulation based analyses.