The altermagnetism influences the electronic states allowing the presence of non-relativistic spin-splittings. Since altermagnetic spin-splitting is present along specific k-paths of the 3D Brillouin zone, we expect that the altermagnetic surface stateswill be present on specific surface orientations. We unveil the properties of the altermagnetic surface states considering three representative materials belonging to the orthorhombic, hexagonal and tetragonal space groups. We calculate the 2D projected Brillouin zone from the 3D Brillouin zone. We study the surfaces with their respective 2D Brillouin zones establishing where the spin-splittings with opposite sign merge annihilating the altermagnetic properties and on which surfaces the altermagnetism is preserved. Looking at the three principal surface orientations, we find that for several cases two surfaces are blind to the altermagnetism, while the altermagnetism survives for one surface orientation. Which surface preserves the altermagnetism depends also on themagnetic order. We qualitatively show that an electric field orthogonal to the blind surface can activate the altermagnetism. Our projection method was proven for strong altermagnetism, but it will be equivalently valid for recently discovered weak altermagnetism. Our results predict which surfaces to cleave in order to preserve altermagnetism in surfaces or interfaces and this paves the way to observe non-relativistic altermagnetic spin-splitting in thin films via spin-resolved ARPES and to interface the altermagnetism with other collective modes. We open future perspectives for the study of altermagnetic effects on the trivial and topological surface states.