This paper presents an innovative eight-pass laser amplifier design that effectively utilizes polarization and angular multiplexing, enjoying high gain, high extraction efficiency, and compact layout. To optimize the design parameters, a general spatiotemporal model for a multi-pass amplifier is established that accounts for beam passages in different angles, and the predicted output energy and gain distribution agree well with the experimental results. The multi-pass amplifier scales the seed energy of 120 mJ to 5 J at 10 Hz and 3 J at 50 Hz, with the beam quality within three times the diffraction limit.