One of the most important open problems in computational molecular biology is the prediction of the conformation of a protein based on its amino acid sequence. In this paper, we design approximation algorithms for structure prediction in the so-called HP side chain model. The major drawback of the standard HP side chain model is the bipartiteness of the cubic lattice. To eliminate this drawback, we introduce the extended cubic lattice which extends the cubic lattice by diagonals in the plane. For this lattice, we present two linear algorithms with approximation ratios of 59/70 and 37/42, respectively. The second algorithm is designed for a ‘natural’ subclass of proteins, which covers more than 99:5% of all sequenced proteins. This is the first time that a protein structure prediction algorithm is designed for a ‘natural’ subclass of all combinatorially possible sequences.