According to Joseph Allen's Mesoamerican theory, the city of Desolation would be located where the present day city of Acayucan in the State of Veracruz is located. Acayucan is near the Olmec ruins of San Lorenzo.
As you drive from Juchitan, Mexico north through the Isthmus of Tehuantepec, a distance of about 110 miles, you will arrive at Acayucan. . . . This road connecting the Gulf of Tehuantepec on the Pacific side and the Gulf of Mexico on the Atlantic side is the old Kings Highway. It is the most passable route from Central America to the northern part of Mexico. To cross into northern Mexico from the Tabasco-Campeche north side is very difficult because of the many river drainages and countless lagoons in that area. To travel directly east to west from Central America to northern Mexico is also very difficult because of the rugged mountain ranges separated by the narrow passage that goes between the two mountain ranges.
The railroad tracks go the same south-north route from Juchitan to Acayucan. Acayucan is about 28 miles from the Gulf of Mexico on the eastward side. [Joseph L. Allen, Exploring the Lands of the Book of Mormon, pp. 231-232] [See Geographical Theory Maps]
Geographical [Theory Map]: Mormon 3:5 The Nephites Gather at Desolation (by the Narrow Pass) (361 A.S.--362 A.S.)
Mormon 3:5 The City of Desolation ([Illustration]): The proposed geographical locations at the A.D. 360 gathering (at Desolation) near the Narrow Neck of Land. [Joseph L. Allen, Exploring the Lands of the Book of Mormon, p. 348]
Mormon 3:5 The City of Desolation ([Illustration]): The proposed location of the A.D. 375 battle between the Nephites and the Lamanites. [Joseph L. Allen, Exploring the Lands of the Book of Mormon, p. 348]
Mormon 3:5 The City of Desolation ([Illustration]): Map illustrating the Nephite cities of Angola, David, Joshua, and Jashon. [Joseph L. Allen, Exploring the Lands of the Book of Mormon, p. 395]
Mormon 3:5 A City which was in the borders, by the narrow pass ([Illustration]): Map #4 shows a number of the ruins which definitely date to the Nephite period located in the general area of these lagoons. The NWAF has reported many other sites without a description of their age. They also reported a number of sites dating to the early Classic time period which begins in A.D. 300. Such sites were not included because they might, but don't necessarily, go back to the time of Mormon. (Delagado, 1965) [David A. Palmer, In Search of Cumorah, pp. 34, 256-257]