ABSTRACTThe mollified uniform distribution is rediscovered, which constitutes a “soft” version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For example, it constitutes a model covering platykurtic, mesokurtic, and leptokurtic shapes. Its cumulative distribution function may also serve as the soft‐clipping response function for defining generalized linear models with approximately linear dependence. Furthermore, it might be considered for teaching, as an appealing example for the convolution of random variables. Finally, a discrete type of mollified uniform distribution is briefly discussed as well.