  We propose a flexible family of distributions, generalized $t$-distributions,
on the cylinder which is obtained as a conditional distribution of a trivariate
$t$ distribution. The new distribution has unimodality or bimodality, symmetry
or asymmetry, depending on the values of parameters and flexibly fits the
cylindrical data. The circular marginal of this distribution is distributed as
a generalized $t$-distribution on the circle. Some other properties are also
investigated. The proposed distribution is applied to the real cylindrical
data.
