Cooking and heating fuels needed for everyday survival is experiencing either dwindling supply, fluctuating prices or difficulty in accessing it, with developing countries being the worst hit, so the poor and low income earners rely greatly on fuelwood to meet their everyday energy needs. Agricultural waste residues can be a reliable alternative to fossil fuels and fuelwood when converted into solid fuels called briquettes, whose quality is determined by the production factors. In this research, a multi-piston binderless briquetting machine was designed, fabricated and tested by producing briquettes from selected biomass wastes (corn cob, sugarcane bagasse, groundnut shell, sawdust and rice husk) and polyethylene wastes (sachet water wastes), using the machine. Experimental run was designed via Taguchi fractional factorial using Minitab 17 software, for 27 runs orthogonal array. Input factors; moulding temperature (250, 270 and 290 0C), Moulding pressure (46, 56 and 66 MPa), composition of polyethylene (10, 20 and 30%) and dwell time (60, 180 and 300 seconds) were varied. From the analysis of the materials and briquettes produced, highest bulk density of the mixed material was 250kg/m3, highest compressed density of the briquettes was 587 kg/m3, highest relaxed density was 545 kg/m3 while highest calorific value was 26.3162 MJ/kg. For proximate analysis, lowest moisture content of the briquettes was 0.04%, lowest volatile matter was 71.63%, lowest ash content was 2.77% and highest fixed carbon was 20.40%. Fuels produced from these selected materials were fuels of good qualities that can provide alternative to fossil fuels and fuelwood.