Disclosed is a high density ethylene polymer comprising a homopolymer of ethylene, or a copolymer of ethylene with at least one comonomer selected from an .alpha.-olefin, a cyclic olefin, and linear, branched and cyclic dienes, and having the following properties: (a) a density d (g/cm.sup.3) of from 0.951 to 0.980; (b) an M.sub.I (g/10 minutes) of more than 3 and not more than 100 (M.sub.I is the melt flow rate as measured at 190.degree. C. under a load of 2.16 kg); (c) the polymer satisfying: log a.sub.kI .gtoreq.-0.844 log M.sub.I +1.462 [M.sub.I is as defined above, and a.sub.kI is the Izod impact strength (kgf.multidot.cm/cm.sup.2)]; (d) the polymer satisfying: log M.sub.IR .gtoreq.-0.094 log M.sub.I +1.520 [M.sub.I is as defined above, and M.sub.IR is the H.sub.MI /M.sub.I ratio in which H.sub.MI (g/10 minutes) is the melt flow rate as measured at 190.degree. C. under a load of 21.6 kg and M.sub.I is as defined above]; and wherein (e) the d (g/cm.sup.3) and the M.sub.I (g/10 minutes) satisfy: d.gtoreq.-0.00873 log M.sub.I +0.972. The ethylene polymer has excellent mechanical properties and excellent moldability, and can be advantageously produced by use of a catalyst comprising (A) a specific transition metal compound containing, as a ligand, an unsubstituted or substituted indenyl group, or di or tri substituted cyclopentadienyl group; (B) an inorganic solid component comprising a particulate inorganic solid having OH groups on a surface thereof and, carried thereon, an organoaluminumoxy compound having an alkyl group; and (C) an organoaluminum compound.