Abstract Compaction of milled walnut shells was carried out at moisture contents of 11.3, 18.3, and 25.3% w.b., material temperatures of 93 °C and 106 °C, agglomerate lengths, la, of 40, 50, 60, 70, and 80 mm and a speed of 100 mm min−1. The phenomenon of friction vibrations occurred at the moisture level of 11.3% w.b. when moving the pellets in die. At a higher temperature of 106 vs. 93 °C the frequencies of the compaction pressure oscillation were lower – 0.16 and 0.21 Hz, respectively, and their vibration amplitudes were also higher – 0.49 and 0.38 MPa, respectively. The relationship between the pellets' compressive strength and the unit pellet density was an inverse for moisture and temperature, and was coherent for the agglomerate length (i.e. die thickness). The good strengths of the pellets with densities higher than 820 kg m−3 were obtained at the moisture level of 18.3% w.b., temperature of 93 °C and an la in the range of 60–70 mm. Using the character correlation method, the set of parameters characterising agglomeration and the pellets were limited from twelve to seven. The novelty of this work lies in the application of spectral analysis and the use of the character correlation method.