It is clear that prisoners have no Fourth Amendment rights against searches of their prison cells.

In Hudson v. Palmer, 468 U.S. 517, 104 S.Ct. 3194, 82 L.Ed.2d 393 (1984), the United States Supreme Court addressed the question of whether the Fourth Amendment applies within a prison cell.  The court held that is does not.

[W]e hold that society is not prepared to recognize as legitimate any subjective expectation of privacy that a prisoner might have in his prison cell and that, accordingly, the Fourth Amendment proscription against unreasonable searches does not apply within the confines of the prison cell.  The recognition of privacy rights for prisoners in their individual cells simply cannot be reconciled with the concept of incarceration and the needs and objectives of penal institutions.

Id. at 526-528, 104 S.Ct. at 3200-3201.

The Hudson Court upheld, against a  Fourth Amendment challenge, a policy permitting random cell searches. 

The uncertainty that attends random searches of cells renders these searches perhaps the most effective weapon of the prison administrator in the constant fight against the proliferation of knives and guns, illicit drugs, and other contraband. The Court of Appeals candidly acknowledged that “the device [of random cell searches] is of obvious utility in achieving the goal of prison security.”

A requirement that even random searches be conducted pursuant to an established plan would seriously undermine the effectiveness of this weapon.  It is simply naive to believe that prisoners would not eventually decipher any plan officials might devise for “planned random searches,” and thus be able routinely to anticipate searches. The Supreme Court of Virginia identified the shortcomings of an approach such as that adopted by the Court of Appeals and the necessity of allowing prison administrators flexibility:

“For one to advocate that prison searches must be conducted only pursuant to an enunciated general policy or when suspicion is directed at a particular inmate is to ignore the realities of prison operation. Random searches of inmates, individually or collectively, and their cells and lockers are valid and necessary to ensure the security of the institution and the safety of inmates and all others within its boundaries. This type of search allows prison officers flexibility and prevents inmates from anticipating, and thereby thwarting, a search for contraband.” Marrero v. Commonwealth, 222 Va. 754, 757, 284 S.E.2d 809, 811 (1981).

We share the concerns so well expressed by the Supreme Court and its view that wholly random searches are essential to the effective security of penal institutions.

Id. at 528-529, 104 S.Ct. at 3201-3202. See also Block v. Rutherford, 468 U.S. 576, 589-591, 104 S.Ct. 3227, 3234-3235, 82 L.Ed.2d 438 (1984) (holding that a county jail's practice of conducting random, irregular shakedown searches of pretrial detainees' cells in the absence of the detainees was a reasonable response by jail officials to legitimate security concerns and did not violate the Due Process Clause of the Fourteenth Amendment); Bell v. Wolfish, 441 U.S. 520, 555-557, 99 S.Ct. 1861, 1882-1884, 60 L.Ed.2d 447 (1979) (holding requirement that pretrial detainees remain outside their cells during routine "shakedown" inspections by prison officials did not violate the Fourth Amendment, but simply facilitated the safe and effective performance of searches); State v. Dulsworth, 781 S.W.2d 277 (Tenn. Crim. App. 1989) (A prisoner does not have a justifiable, reasonable or legitimate expectation of privacy that is subject to invasion by law enforcement officers, as the United States Supreme Court ruled in Hudson v. Palmer, 468 U.S. 517, 104 S.Ct. 3194, 82 L.Ed.2d 393 (1984)); State v. Gant, 537 S.W.2d 711 (Tenn. Crim. App. 1975) (We think it is recognized that, for safety and security purposes, prison officials are authorized to search a prisoner's cell without a warrant for weapons.).