The subject matter of the study is the encryption of information in cloud data computation and storage. Cloud technologies enable reducing the cost of IT infrastructure significantly and responding to changes in computing needs flexibly. In this case, the possibilities to perform calculations on the encrypted data without decrypting should be provided. Fully homomorphic encryption has this feature. The goal of this article is to increase the efficiency of fully homomorphic encryption (FHE) on the basis of matrix polynomials using the method of batch encryption to one ciphertext of several plaintexts with the subsequent complex processing of encrypted data. Batch encryption comes down to the fact that while conducting the operation on two ciphertexts, operations are simultaneously conducted coordinatewise on all the data contained in these ciphertexts in the form of plaintexts (SIMD). The task is the construction of algorithms of fully homomorphic data encryption using matrix polynomials. The following encryption methods are used in the article: the use of the Chinese remainder theorem; recording several different eigenvalues with different eigenvectors to the same matrix; the interpolation of matrix polynomials. The following results were obtained: possible approaches to constructing a batch EHE on the basis of matrix polynomials were described and analyzed, a set of algorithms that implement the FHE crypto scheme with interpolation of matrix polynomials was presented. The above algorithms and crypto schemes enable transmitting information in messages and data in queries as a plain text because an unlimited number of complex algebraic operations can be performed on the encrypted data, which makes it difficult to decrypt and read data without the knowledge of the entire algorithm. The constructed crypto schemes were shown as more efficient than analogues developed by IBM researchers. The following conclusion can be made: a batch fully homomorphic encryption using matrix polynomials can eliminate the need for at least partial decryption of data to carry out unauthorized computation on encrypted cloud data arrays.