The paper presents methods for spline interpolation preserving the shape of the data (monotonicity and convexity) by using discrete weighted cubic splines. One considers the data \((x_i,f_i),\, i=0,1,\dots,N+1,\) \(a=x_00\)) coincide. For \(\tau_i=0\) one obtains cubic splines of class \(C^1.\) In Theorem 1, imposing the boundary conditions \(S'(x_0)=f'_0,\, S'(x_{N+1})=f'_{N+1}\) to a function \(f\in C^4[a,b]\), one obtains error estimations for \(\|S^{(r)}(x)-f^{(r)}(x)\|_\infty,\, r=0,1.\) In Theorems 3 and 4 one obtains sufficient conditions for preserving the monotonicity, respectively the convexity, of the data \(\{f_i\}.\) One gives two algorithms with automatic selection of the shape control parameters. Discrete weighted cubic \(B\)-splines, control point approximation and graphical examples are considered as well.