Acceptance sampling is one of the major components of the field of statistical quality control. It is primarily used for the inspection of incoming or outgoing lots. In recent years, it has become typical to work with suppliers to improve their process performance through the use of statistical process control (SPC). Acceptance sampling refers to the application of specific sampling plans to a designated lot or sequence of lots. Acceptance sampling procedures can, however, be used in a program of acceptance control to achieve better quality at lower cost, improved control, and increased productivity. In some cases, it may not be possible to define acceptance sampling parameters as crisp values. Especially in production environments, it may not be easy to define the parameters fraction of nonconforming, acceptance number, or sample size as crisp values. In these cases, these parameters can be expressed by linguistic variables. The fuzzy set theory can be used successfully to cope the vagueness in these linguistic expressions for acceptance sampling. In this paper, the two main distributions of acceptance sampling plans which are binomial and Poisson distributions are handled with fuzzy parameters and their acceptance probability functions are derived. Then fuzzy acceptance sampling plans are derived based on these distributions.