Neutral strongly interacting massive particles (SIMPs) were searched for at the Gran Sasso National Laboratory by using two "planes" of detectors in the Ӎ100 kg highly radiopure NaI(Tl) DAMA setup. SIMP exclusion plots and model-independent limits on neutral nuclearites have been significantly improved. PACS numbers: 95.35. + d, 12.38.Mh, 29.40.Mc In this paper we present results on a further search for neutral strongly interacting massive particles (SIMPs), that is, neutral particles with masses ͑M S ͒ between few GeV and the grand unified theory scale and cross sections on protons ͑s p ͒ up to Ӎ10 222 cm 2 , embedded in the galactic halo (therefore, with b Ӎ 10 23 ). Candidates of this kind could be formed, e.g., by the "neutralization" of exotic particles (with electromagnetic and/or nuclear charge) with ordinary matter during primordial nucleosynthesis; therefore, they have also been investigated by searching for anomalous heavy nuclei in terrestrial samples [1]. Moreover, it has been suggested that SIMPs could be the sources of ultrahigh-energy cosmic rays [2] and that in some models of supersymmetry breaking they could appear as, e.g., gluino lightest supersymmetric particles [3]. In spite of their large cross sections, SIMPs [4,5] should have a relatively low interaction rate due to their low density in the galactic halo. Some discussion on possible abundance and cosmological interest can be found in Ref. [6]. A detailed analysis of the available data was performed in Ref. [7] Starkman et al.; further limits on s p versus M S have then been achieved in Refs. [8-10].The present result has been obtained by searching for delayed coincidences between two "planes" of detectors in the Ӎ100 kg NaI(Tl) dark matter (DAMA) experimental setup [11-17] during 350.05 days. The setup is placed deep underground in the Gran Sasso National Laboratory of INFN [18] at 42 ± 27' north latitude, and it is shielded from cosmic rays by a rock depth of about 3400 mwe (meter of water equivalent). The overlaying rock degrades the SIMPs energy and reduces the setup sensitivity to large cross sections, but the low background technique and the m flux reduction allow the SIMPs search to be extended to lower fluxes and higher masses.In the following we also utilize the data previously collected at Gran Sasso with another of our setups, the one named F in Ref.[10], while we do not consider here the data we obtained with the test setups ͑P 1 , P 2 ͒ described in Ref.[9], because of both the marginal statistics and the higher energy threshold.Finally, the experimental data are also used to set improved model-independent upper limits on the flux of neutral nuclearites.Experimental procedure and results.-Following the suggestion of Ref.[4] and according to Refs. [9,10], two parallel planes-each one made up of three 9.70 kg (10.2-cm large, 10.2-cm thick, and 25.4-cm long) low radioactive NaI(Tl) detectors-have been used to search for delayed coincidences from SIMP elastic scattering on sodium and/or iodine nuclei during 350.05 days; the mea...