An approximate solution of inner boundary value problems with a shift of the following type \(F^+[\alpha (t)]-a(t)F^+(t)- b(t)\overline{F^+(t)}=g(t)\), \(t\in L\) is given by means of collocation and reduction methods. Here L is the unit circle of the complex plane, a, b, g, \(\alpha '\in H_{\lambda}^{(r)}\), \(0<\lambda <1\), r is a nonnegative integer, \(\alpha\) ’(t)\(\neq 0\), \(\alpha\) [\(\alpha\) (t)]\(\equiv t\) and \(F^+\) is the unknown analytic function in the inside of L.