  We discuss low-lying collective excitations of $\Lambda$ hypernuclei using
the self-consistent mean-field approaches. We first discuss the deformation
properties of $\Lambda$ hypernuclei in the $sd$-shell region. Based on the
relativistic mean-field (RMF) approach, we show that the oblate deformation for
$^{28}$Si nucleus may disappear when a $\Lambda$ particle is added to this
nucleus. We then discuss the rotational excitations of $^{25}_{\Lambda}$Mg
nucleus using the three-dimensional potential energy surface in the deformation
plane obtained with the Skyrme-Hartree-Fock method. The deformation of
$^{25}_{\Lambda}$Mg nucleus is predicted to be slightly reduced due to an
addition of $\Lambda$ particle. We demonstrate that this leads to a reduction
of electromagnetic transition probability, $B(E2)$, in the ground state
rotational band. We also present an application of random phase approximation
(RPA) to hypernuclei, and show that a new dipole mode, which we call a soft
dipole $\Lambda$ mode, appears in hypernuclei, which can be interpreted as an
oscillation of $\Lambda$ particle against the core nucleus.
