  Let $\mathcal{A}$ denote the class of all analytic functions $f$ defined in
the open unit disc $\mathbb{D}$ with the normalization $f(0)=0=f'(0)-1$ and let
$P'$ be the class of functions $f\in\mathcal{A}$ such that
${\rm{Re}}\,f'(z)>0$, $z\in\mathbb{D}$. In this article, we obtain radii of
concavity of $P'$ and for the class $P'$ with the fixed second coefficient.
After that, we consider linearly invariant family of functions, along with the
class of starlike functions of order $1/2$ and investigate their radii of
concavity. Next, we obtain a lower bound of radius of concavity for the class
of functions $\mathcal{U}_0(\lambda)=~\{f\in\mathcal{U}(\lambda) : f''(0)=0\}$,
where
  $$
  \mathcal{U}(\lambda)=\left\{f\in\mathcal{A} :
\left|\left(\frac{z}{f(z)}\right)^2f'(z)-1\right|<\lambda,~z\in
\mathbb{D}\right\},\quad \lambda \in (0,1].
  $$
  We also investigate the meromorphic analogue of the class
$\mathcal{U}(\lambda)$ and compute its radius of concavity.
