In the linear cryptanalysis (LC), to decrease the number of plain/cipher text pairs required for successful attack against DES, it is necessary to improve the effectiveness of the linear approximate expression and to decrease the number of key bits in the expression to be exhaustively searched for. In the previous work, we proposed a linear sieve method to improve the effectiveness of the linear approximate expression. On the other hand, the number of key bits increased. To suppress the number of key bits, we propose Fixed Sieve Linear Cryptanalysis (FS-LC) with fixed sieve key of the linear sieve method. With FS-LC against 8-round DES, we showed the number of plain/cipher text pairs required for sucessful attack is less than that of LC. Furthmore, we extended FS-LC with Kaliski's techniques using the multiple linear approximate expressions to intoroduce Fixed Sieve multiple Linear Cryptanalysis (FS-mLC). With FS-mLC against 8-round DES, computer simulation revealed that it is possible to solve its encryption-key with 220 plain/cipher text pairs. The number of pairs is about a half of the Matsui's 1-round linear cryptanalysis cases.